17 results

A $675 stereo receiver loses value at a rate of about $18 per month The equation y = 675 - 18x repre

A $675 stereo receiver loses value at a rate of about $18 per month The equation y = 675 - 18x represents the value of the receiver after x months. Identify and interpret the x- and y-intercepts. Explain how you can use the intercepts to help you graph the equation
y = 675 - 18x
The y-intercept is found when x is 0:
y = 675 - 18(0)
y = 675 - 0
y = 675
The x-intercept is found when y is 0:
0 = 675 - 18x
[URL='https://www.mathcelebrity.com/1unk.php?num=675-18x%3D0&pl=Solve']Typing this equation into our search engine[/URL], we get:
x = 37.5

A line has a slope of 7 and a y-intercept of -4. What is its equation in slope intercept form

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]

Big John weighs 300 pounds and is going on a diet where he'll lose 3 pounds per week. Write an equat

Big John weighs 300 pounds and is going on a diet where he'll lose 3 pounds per week. Write an equation in slope-intercept form to represent this situation.
[LIST]
[*]The slope intercept form is y = mx + b
[*]y is John's weight
[*]x is the number of weeks
[*]A 3 pound per week weight loss means -3 as the coefficient m
[*]b = 300, John's starting weight
[/LIST]
[B]y = -3x + 300[/B]

Can a coefficient of determination be negative? Why or why not?

Can a coefficient of determination be negative? Why or why not?
[B]Yes, reasons below[/B]
[LIST]
[*] predictions that are being compared to the corresponding outcomes have not been derived from a model-fitting procedure using those data
[*] where linear regression is conducted without including an intercept
[*] Yes, negative values of R2 may occur when fitting non-linear functions to data
[/LIST]

Ellipses

Free Ellipses Calculator - Given an ellipse equation, this calculates the x and y intercept, the foci points, and the length of the major and minor axes as well as the eccentricity.

Equation 2y+5x=40. Interprt the intercepts

Equation 2y+5x=40. Interprt the intercepts
Y intercept is when X = 0
2y + 5(0) = 40
2y = 40
Divide each side by 2
[B]y = 20
[/B]
X intercept is when Y = 0
2(0) + 5x = 40
5x = 40
Divide each side by 5
[B]x = 8[/B]

Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and

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]

Function

Free Function Calculator - Takes various functions (exponential, logarithmic, signum (sign), polynomial, linear with constant of proportionality, constant, absolute value), and classifies them, builds ordered pairs, and finds the y-intercept and x-intercept and domain and range if they exist. Table of Functions Calculator

Hyperbola

Free Hyperbola Calculator - Given a hyperbola equation, this calculates:

* Equation of the asymptotes

* Intercepts

* Foci (focus) points

* Eccentricity ε

* Latus Rectum

* semi-latus rectum

* Equation of the asymptotes

* Intercepts

* Foci (focus) points

* Eccentricity ε

* Latus Rectum

* semi-latus rectum

is parallel to the x-axis and has an y-intercept of 3

is parallel to the x-axis and has an y-intercept of 3
Parallel to the x axis means it runs through the y-axis
y-intercept of 3 means our equation is [B]y = 3[/B]

Kayla has $1500 in her bank account. She spends $150 each week. Write an equation in slope-intercept

Kayla has $1500 in her bank account. She spends $150 each week. Write an equation in slope-intercept form that represents the relationship between the amount in Kayla's bank account, A, and the number of weeks she has been spending, w
[LIST]
[*]Slope intercept form is written as A = mw + b
[*]m = -150, since spending is a decrease
[*]b = 1500, since this is what Kayla starts with when w = 0
[/LIST]
[B]A = -150w + 1500[/B]

Line Equation-Slope-Distance-Midpoint-Y intercept

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

* 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

Quadratic Equations and Inequalities

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax^{2} + bx + c = 0. Also generates practice problems as well as hints for each problem.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)^{2} + k

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

* Solve using the quadratic formula and the discriminant Δ

* Complete the Square for the Quadratic

* Factor the Quadratic

* Y-Intercept

* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)

* Concavity of the parabola formed by the quadratic

* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

slope is 0 and whose y-intercept is 9.

slope is 0 and whose y-intercept is 9.
The standard line equation is y = mx + b where m is the slope and b is the y-intercept is b.
Plugging in our numbers, we get:
y = 0x + 9
y = [B]9[/B]

The graph of a polynomial f(x) = (2x - 3)(x - 4)(x + 3) has x-intercepts at 3 values. What are they?

The graph of a polynomial f(x) = (2x - 3)(x - 4)(x + 3) has x-intercepts at 3 values. What are they?
A few things to note:
[LIST]
[*]X-intercepts are found when y (or f(x)) is 0.
[*]On the right side, we have 3 monomials.
[*]Therefore, y or f(x) could be 0 when [U]any[/U] of these monomials is 0
[/LIST]
The 3 monomials are:
[LIST=1]
[*]2x - 3 = 0
[*]x - 4 = 0
[*]x + 3 = 0
[/LIST]
Find all 3 x-intercepts:
[LIST=1]
[*]2x - 3 = 0. [URL='https://www.mathcelebrity.com/1unk.php?num=2x-3%3D0&pl=Solve']Using our equation calculator[/URL], we see that x = [B]3/2 or 1.5[/B]
[*]x - 4 = 0 [URL='https://www.mathcelebrity.com/1unk.php?num=x-4%3D0&pl=Solve']Using our equation calculator[/URL], we see that x = [B]4[/B]
[*]x + 3 = 0 [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B3%3D0&pl=Solve']Using our equation calculator[/URL], we see that x = [B]-3[/B]
[/LIST]
So our 3 x-intercepts are:
x = [B]{-3, 3/2, 4}[/B]

What is a Function

Free What is a Function Calculator - This lesson walks you through what a function is, how to write a function, the part of a function, and how to evaluate the outputs of a function.

This lesson also shows you the domain and range of a function. This lesson shows you the y-intercept of a function and the x-intercept of a function. Also shows Relation and function

This lesson also shows you the domain and range of a function. This lesson shows you the y-intercept of a function and the x-intercept of a function. Also shows Relation and function

Write an equation in slope-intercept form for the line with slope 4 and y-intercept -7

Write an equation in slope-intercept form for the line with slope 4 and y-intercept -7
The standard equation for slope (m) and y-intercept (b) is given as:
y = mx + b
We're given m = 4 and y-intercept = -7, so we have:
[B]y = 4x - 7[/B]