Free 2 Lines Intersection Calculator - Enter any 2 line equations, and the calculator will determine the following:
* Are the lines parallel?
* Are the lines perpendicular
* Do the lines intersect at some point, and if so, which point?
* Is the system of equations dependent, independent, or inconsistent

A $654,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by y = 654,000 ? 1800x dollars. After how many months will the value of the building be $409,200? We want to know x for the equation: 654000 - 1800x = 409200 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=654000-1800x%3D409200&pl=Solve']type it in our math engine[/URL] and we get: x = [B]136 months[/B]

A 100 point test contains a total of 20 questions. The multiple choice questions are worth 3 points each and short response questions are worth 8 points each. Write a system of linear equations that represents this situation Assumptions: [LIST] [*]Let m be the number of multiple choice questions [*]Let s be the number of short response questions [/LIST] Since total points = points per problem * number of problems, we're given 2 equations: [LIST=1] [*][B]m + s = 20[/B] [*][B]3m + 8s = 100[/B] [/LIST] We can solve this system of equations 3 ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get: [B]m = 12, s = 8[/B]

A Bouquet of lillies and tulips has 12 flowers. Lillies cost $3 each, and tulips cost $2 each. The bouquet costs $32. Write and solve a system of linear equations to find the number of lillies and tulips in the bouquet. Let l be the number of lillies and t be the number of tulips. We're given 2 equations: [LIST=1] [*]l + t = 12 [*]3l + 2t = 32 [/LIST] With this system of equations, we can solve it 3 ways. [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter which method we choose, we get: [LIST] [*][B]l = 8[/B] [*][B]t = 4[/B] [/LIST] [B]Now Check Your Work For Equation 1[/B] l + t = 12 8 + 4 ? 12 12 = 12 [B]Now Check Your Work For Equation 2[/B] 3l + 2t = 32 3(8) + 2(4) ? 32 24 + 8 ? 32 32 = 32

A candlestick burns at a rate of 0.2 inches per hour. After eight straight hours of burning, the candlestick is 13.4 inches tall. Write and solve a linear equation to find the original height of the candle. Let h equal the number of hours the candlestick burns. We have a candlestick height equation of C. C = 13.4 + 0.2(8) <-- We need to add back the 8 hours of candlestick burning C = 13.4 + 1.6 C = [B]15 inches[/B]

A family buys airline tickets online. Each ticket costs $167. The family buys travel insurance with each ticket that costs $19 per ticket. The Web site charges a fee of $16 for the entire purchase. The family is charged a total of $1132. How many tickets did the family buy? Let t be the number of tickets. We have the following equation with ticket price, insurance, and flat fee: 167t + 19t + 16 = 1132 Combine like terms: 186t + 16 = 1132 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=186t%2B16%3D1132&pl=Solve']equation calculator[/URL], we have: [B]t = 6[/B]

A group of campers have 250 pounds of food. They plan to eat 12 pounds a day. How many days will it take them to eat the food. Write your answer in a linear equation. Let the number of days be d. We have the following equation: 12d = 250 To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=12d%3D250&pl=Solve']type this equation in our search engine[/URL] and we get: d = [B]20.833[/B]

A line has a slope of 7 and a y-intercept of -4. What is its equation in slope intercept form The slope-intercept equation for a line: y = mx + b where m is the slope Given m = 7, we have: y = 7x + b The y-intercept is found by setting x to 0: y = 7(0) + b y = 0 + b y = b We're given the y-intercept is -4, so we have: b = -4 So our slope-intercept equation is: [B]y = 7x - 4[/B]

A line in the xy-plane passes through the origin and has a slope of 4/5. What points lie on that line. Our line equation is: y = mx + b We're given: m = 4/5 (x, y) = (0, 0) So we have: 0 = 4/5(0) + b 0 = 0 + b b = 0 Therefore, our line equation is: y = 4/5x [URL='https://www.mathcelebrity.com/function-calculator.php?num=y%3D4%2F5x&pl=Calculate']Start plugging in values here to get a list of points[/URL]

A line passes through the point -3,4 and has a slope of -5 Using our [URL='http://A line passes through the point -3,4 and has a slope of -5']point slope calculator[/URL], we get a line equation of: y = -5x - 11

A mother gives birth to a 10 pound baby. Every 2 months, the baby gains 5 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight. If the baby gains 5 pounds every 2 months, then they gain 5/2 = 2.5 pounds per month. Let x be the number of months old for the baby, we have: The baby starts at 10 pounds. And every month (x), the baby's weight increases 2.5 pounds. Our equation is: [B]y = 2.5x + 10[/B]

A mother gives birth to a 6 pound baby. Every 4 months, the baby gains 4 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx b that describes the baby's weight. The baby gains 4 pounds every month, where x is the number of months since birth. The baby boy starts life (time 0) at 6 pounds. So we have [B]y = 4x + 6[/B]

A mother gives birth to a 7 pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight. Every month, the baby gains 2/3 of a pound. So we have: [B]y = 2/3x + 7 [/B] The baby starts off with 7 pounds. So we add 7 pounds + 2/3 times the number of months passed since birth.

A music app charges $2 to download the app plus $1.29 per song download. Write and solve a linear equation to find the total cost to download 30 songs Set up the cost function C(s) where s is the number of songs: C(s) = cost per song * s + download fee Plugging in our numbers for s = 30 and a download fee of $2 and s = 1.29, we have: C(30) = 1.29(30) + 2 C(30) = 38.7 + 2 C(30) = [B]40.7[/B]

A music app charges $2 to download the app plus $1.29 per song downloaded. Write and solve a linear equation to find the total cost to download 30 songs. Let the number of songs be s. And the cost function be C(s). We have: C(s) = Price per song downloaded * s + app download charge C(s) = 1.29s + 2 The problem asks for C(30): C(3) = 1.29(30) + 2 C(3) = 38.7 +2 C(3) = $[B]40.7[/B]

a music app charges $5 to download the app plus $1.25 per song downloaded. write linear equation to calculate the cost for x number of songs With x songs, our Cost equation C(x) is: C(x) = cost per download * x downloads + app download fee [B]C(x) = 1.25x + 5[/B]

A music app charges 2$ to download the app plus 1.29$ per song download. Write and solve linear equation and a linear equation to find the total cost to download 30 songs Set up the equation C(d) where d is the number of downloads: C(d) = cost per download * d + download fee Plugging in our numbers, we get: C(d) = 1.29d + 2 The problem asks for C(30): C(30) = 1.29(30) + 2 C(30) = 38.7 + 2 C(30) = [B]40.70[/B]

A straight line has the equation ax + by=23. The points (5,-2) and (1,-5) lie on the line. Find the values of a and b. plug in both points and form 2 equations: [LIST=1] [*]5a - 2b = 23 [*]1x - 5b = 23 [/LIST] We can solve this simultaneous equations any one of three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5a+-+2b+%3D+23&term2=1a+-+5b+%3D+23&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5a+-+2b+%3D+23&term2=1a+-+5b+%3D+23&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5a+-+2b+%3D+23&term2=1a+-+5b+%3D+23&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [LIST] [*][B]a = 3[/B] [*][B]b = -4[/B] [/LIST]

A yoga member ship costs $16 and additional $7 per class. Write a linear equation modeling the cost of a yoga membership? Set up the cost function M(c) for classes (c) [B]M(c) = 16 + 7c[/B]

Angie and Kenny play online video games. Angie buy 2 software packages and 4 months of game play. Kenny buys 1 software package and 1 month of game play. Each software package costs $25. If their total cost is $155, what is the cost of one month of game play. Let s be the cost of software packages and m be the months of game play. We have: [LIST] [*]Angie: 2s + 4m [*]Kenny: s + m [/LIST] We are given each software package costs $25. So the revised equations above become: [LIST] [*]Angie: 2(25) + 4m = 50 + 4m [*]Kenny: 25 + m [/LIST] Finally, we are told their combined cost is 155. So we add Angie and Kenny's costs together: 4m + 50 + 25 + m = 155 Combine like terms: 5m + 75 = 155 [URL='http://www.mathcelebrity.com/1unk.php?num=5m%2B75%3D155&pl=Solve']Typing this into our search engine[/URL], we get [B]m = 16[/B]

Free Budget Line Equation Calculator - Solves for any one of the 5 items in the standard budget line equation:
Income (I)
Quantity of x = Q_x
Quantity of y = Q_y
Price of x = P_x
Price of y = P_y

Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months. Let m be the number of months. We have the pages written function P(m) as: P(m) = 12m + 35 The problem asks for P(5): P(5) = 12(5) + 35 P(5) = 60 + 35 P(5) = [B]95[/B]

Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months. Set up the equation where m is the number of months: pages per month * m + pages written already 12m + 35 The problems asks for m = 5: 12(5) + 35 60 + 35 [B]95 pages[/B]

Choose the equation of a line in standard form that satisfies the given conditions. perpendicular to 4x + y = 8 through (4, 3). Step 1: Find the slope of the line 4x + y = 8. In y = mx + b form, we have y = -4x + 8. The slope is -4. To be perpendicular to a line, the slope must be a negative reciprocal of the line it intersects with. Reciprocal of -4 = -1/4 Negative of this = -1(-1/4) = 1/4 Using our [URL='https://www.mathcelebrity.com/slope.php?xone=4&yone=3&slope=+0.25&xtwo=3&ytwo=2&bvalue=+&pl=You+entered+1+point+and+the+slope']slope calculator[/URL], we get [B]y = 1/4x + 2[/B]

Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and sharing the same y-intercept Get this in slope-intercept form by adding 5y to each side: 4x - 5y + 5y = 5y + 20 Cancel the 5y's on the left side and we get: 5y + 20 = 4x Subtract 20 from each side 5y + 20 - 20 = 4x - 20 Cancel the 20's on the left side and we get: 5y = 4x - 20 Divide each side by 5: 5y/5 = 4x/5 - 4 y = 4x/5 - 4 So we have a slope of 4/5 to find our y-intercept, we set x = 0: y = 4(0)/5 - 4 y = 0 - 4 y = -4 If we want a line perpendicular to the line above, our slope will be the negative reciprocal: The reciprocal of 4/5 is found by flipping the fraction making the numerator the denominator and the denominator the numerator: m = 5/4 Next, we multiply this by -1: -5/4 So our slope-intercept of the perpendicular line with the same y-intercept is: [B]y = -5x/4 - 4[/B]

Find a linear function f, given f(16)=-2 and f(-12)=-9. Then find f(0). We've got 2 points: (16, -2) and (-12, -9) Calculate the slope (m) of this line using: m = (y2 - y1)/(x2 - x1) m = (-9 - -2)/(-12 - 16) m = -7/-28 m = 1/4 The line equation is denoted as: y = mx + b Let's use the first point (x, y) = (16, -2) -2 = 1/4(16) + b -2 = 4 + b Subtract 4 from each side, and we get: b = -6 So our equation of the line is: y = 1/4x - 6 The questions asks for f(0): y = 1/4(0) - 6 y = 0 - 6 [B]y = -6[/B]

Find an equation of the line containing the given pair of points (1,5) and (3,6). Using our[URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=5&slope=+2%2F5&xtwo=3&ytwo=6&pl=You+entered+2+points'] point slope calculator[/URL], we get: [B]y = 1/2x + 9/2[/B]

Find the gradient of the the line with the equation 8x - 4y =12 [URL='https://www.mathcelebrity.com/parperp.php?line1=8x-4y%3D12&line2=6x+-+3y+%3D+18&pl=Slope']Type this equation into our search engine[/URL] and choose "slope" and we get: Slope (gradient) = [B]2[/B]

Find y if the line through (1, y) and (2, 7) has a slope of 4. Given two points (x1, y1) and (x2, y2), Slope formula is: slope = (y2 - y1)/(x2 - x1) Plugging in our coordinates and slope to this formula, we get: (7 - y)/(2 - 1) = 4 7 - y/1 = 4 7 - y = 4 To solve this equation for y, w[URL='https://www.mathcelebrity.com/1unk.php?num=7-y%3D4&pl=Solve']e type it in our search engine[/URL] and we get: y = [B]3[/B]

If the equation of a line passes through the points (1, 3) and (0, 0), which form would be used to write the equation of the line? [URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=3&slope=+&xtwo=0&ytwo=0&bvalue=+&pl=You+entered+2+points']Typing (1,3),(0,0) into the search engine[/URL], we get a point-slope form: [B]y - 3 = 3(x - 1)[/B] If we want mx + b form, we have: y - 3 = 3x - 3 Add 3 to each side: [B]y = 3x[/B]

Joel bought 88 books. Some books cost $13 each and some cost $17 each. In all, he spent $128. Which system of linear equations represents the given situation? Let a be the number of the $13 book, and b equal the number of $17 books. We have the following system of linear equations: [LIST=1] [*][B]a + b = 88[/B] [*][B]13a + 17b = 128[/B] [/LIST] To solve this system, use our calculator for the following methods: [LIST] [*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Substitution']Substitution[/URL] [*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Elimination']Elimination[/URL] [*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Cramers+Method']Cramers Method[/URL] [/LIST]

kim and jason just had business cards made. kim’s printing company charged a one time setup fee of $8 and then $20 per box of cards. jason,meanwhile ordered his online. they cost $8 per box. there was no setup fee, but he had to pay $20 to have his order shipped to his house. by coincidence, kim and jason ended up spending the same amount on their business cards. how many boxes did each buy? how much did each spend? Set up Kim's cost function C(b) where b is the number of boxes: C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee C(b) = 20c + 8 + 0 Set up Jason's cost function C(b) where b is the number of boxes: C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee C(b) = 8c + 0 + 20 Since Kim and Jason spent the same amount, set both cost equations equal to each other: 20c + 8 = 8c + 20 [URL='https://www.mathcelebrity.com/1unk.php?num=20c%2B8%3D8c%2B20&pl=Solve']Type this equation into our search engine[/URL] to solve for c, and we get: c = 1 How much did they spend? We pick either Kim's or Jason's cost equation since they spent the same, and plug in c = 1: Kim: C(1) = 20(1) + 8 C(1) = 20 + 8 C(1) = [B]28 [/B] Jason: C(1) = 8(1) + 20 C(1) = 8 + 20 C(1) = [B]28[/B]

Lebron James scored 288 points in 9 games this season. Assuming he continues to score at this constant rate, write a linear equation that represents the scenario. 288 points / 9 games = 32 points per game Let g be the number of games Lebron plays. We build an equation for his season score: Lebron's Season Score = Points per game * number of games Lebron's Season Score = [B]32g[/B]

Free Line Equation-Slope-Distance-Midpoint-Y intercept Calculator - Enter 2 points, and this calculates the following:
* Slope of the line (rise over run) and the line equation y = mx + b that joins the 2 points
* Midpoint of the two points
* Distance between the 2 points
* 2 remaining angles of the rignt triangle formed by the 2 points
* y intercept of the line equation
* Point-Slope Form
* Parametric Equations and Symmetric Equations

Or, if you are given a point on a line and the slope of the line including that point, this calculates the equation of that line and the y intercept of that line equation, and point-slope form.

Also allows for the entry of m and b to form the line equation

m is the midpoint of cf for points c(3,4) and f(9,8). Find MF Using our [URL='https://www.mathcelebrity.com/slope.php?xone=3&yone=4&slope=+2%2F5&xtwo=9&ytwo=8&pl=You+entered+2+points']line equation and midpoint calculator[/URL], we get: MF = [B](6, 6)[/B]

Free Plane and Parametric Equations in R³ Calculator - Given a vector A and a point (x,y,z), this will calculate the following items:
1) Plane Equation passing through (x,y,z) perpendicular to A
2) Parametric Equations of the Line L passing through the point (x,y,z) parallel to A

Sarah starts with $300 in her savings account. She babysits and earns $30 a week to add to her account. Write a linear equation to model this situation? Enter your answer in y=mx b form with no spaces. Let x be the number of hours Sarah baby sits. Then her account value y is: y = [B]30x + 300[/B]

Free Security Market Line and Treynor Ratio Calculator - Solves for any of the 4 items in the Security Market Line equation, Risk free rate, market return, Β, and expected return as well as calculate the Treynor Ratio.

[IMG]https://mathcelebrity.com/community/data/attachments/0/supp-angles.jpg[/IMG] The angle with measurements of 148 degrees lies on a straight line, which means it's supplementanry angle is: 180 - 148 = 32 Since the angle of 2x - 16 and 32 lie on a straight line, their angle sum equals 180: 2x + 16 + 32 = 180 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B16%2B32%3D180&pl=Solve']type it in our math engine [/URL]and we get: x = [B]66[/B]

Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 20 gallons of fuel, the airplane weighs 2012 pounds. When carrying 55 gallons of fuel, it weighs 2208 pounds. How much does the airplane weigh if it is carrying 65 gallons of fuel? Linear functions are written in the form of one dependent variable and one independent variable. Using g as the number of gallons and W(g) as the weight, we have: W(g) = gx + c where c is a constant We are given: [LIST] [*]W(20) = 2012 [*]W(55) = 2208 [/LIST] We want to know W(65) Using our givens, we have: W(20) = 20x + c = 2012 W(55) = 55x + c = 2208 Rearranging both equations, we have: c = 2012 - 20x c = 2208 - 55x Set them both equal to each other: 2012 - 20x = 2208 - 55x Add 55x to each side: 35x + 2012 = 2208 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=35x%2B2012%3D2208&pl=Solve']equation solver[/URL], we see that x is 5.6 Plugging x = 5.6 back into the first equation, we get: c = 2012 - 20(5.6) c = 2012 - 112 c = 2900 Now that we have all our pieces, find W(65) W(65) = 65(5.6) + 2900 W(65) = 264 + 2900 W(65) = [B]3264[/B]

the equation of a line is y = mx + 4. find m if the line passes through (-5,0) Plug in our numbers of x = -5, and y = 0: -5m + 4 = 0 To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=-5m%2B4%3D0&pl=Solve']plug in this equation into our search engine[/URL] and we get: [B]m = 0.8 or 4/5[/B] so our line equation becomes: [B]y = 4/5x + 4[/B]

Which of the following equations represents a line that is parallel to the line with equation y = -3x + 4? A) 6x + 2y = 15 B) 3x - y = 7 C) 2x - 3y = 6 D) x + 3y = 1 Parallel lines have the same slope, so we're looking for a line with a slope of 3, in the form y = mx + b. For this case, we want a line with a slope of -3, like our given line. If we rearrange A) by subtracting 6x from each side, we get: 2y = -6x + 15 Divide each side by 2, we get: y = -3x + 15/2 This line is in the form y = mx + b, where m = -3. So our answer is [B]A[/B].