Are -4y=3x+4 and y=-4/3x+8:
parallel, intersect, or perpendicular
Get Eq. 1 into y = mx + b format:
-4y = + 3x + 4
| -4y |
| -4 |
| = |
| + 3x + 4 |
| -4 |
y = - 0.75x - 1
Final Answer
You have 2 free calculationss remaining
Standard Equation
Since this equation is in standard y = mx + b format
our line equation is:
y = - 1.3333333333333x + 8
Final Answer
You have 2 free calculationss remaining
Set EQ1 = EQ2:
- 0.75x - 1 = - 1.3333333333333x + 8
-0.75x - -1.3333333333333x = 8 - -1
+ 0.58333333333333x = 9
x = 9/ + 0.58333333333333
x = 15.428571428571
Plug x into equation 1
y = -0.75 * (15.428571428571) - 1
y = -11.571428571429 - 1
y = -12.5714
Our intersection point = (15.428571428571, -12.5714)
Calculate the product of the 2 slopes:
Slope 1 * Slope 2 = -0.75 * -1.3333333333333 = 1
Perpendicular Check
Since the product of the 2 slopes ≠ -1
The lines are not perpendicular
Line Relation Check
The 2 lines intersect at (15.428571428571, -12.5714)
Check if equations are Independent:
Since the slopes are different
The systems are independent
Check if equations are Dependent:
To be dependent
the slopes and y-intercept must be the same.
This is not the case
Check if equations are Inconsistent:
To be inconsistent
The slopes must be the same
Ty-intercepts must different.
This is not the case
Calculate the angle θ
θ is formed by the two lines
| tan(θ) = | m2 - m1 |
| 1 + m2m1 |
| tan(θ) = | -1.3333333333333 --0.75 |
| 1 + -1.3333333333333 *-0.75 |
| tan(θ) = | -0.58333333333333 |
| 1 + 1 |
| tan(θ) = | -0.58333333333333 |
| 2 |
tan(θ) = -0.29166666666667
θ = -16.2602
What is the Answer?
How does the 2 Lines Intersection Calculator work?
* 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
This calculator has 2 inputs.
What 3 formulas are used for the 2 Lines Intersection Calculator?
Lines are perpendicular when they have slopes which are negative reciprocals.
For a line y = mx + b, m is the slope
For more math formulas, check out our Formula Dossier
What 6 concepts are covered in the 2 Lines Intersection Calculator?
- 2 lines intersection
- intersect
- line equation
- parallel
- perpendicular
- two lines which intersect to form a right angle
- slope
- Change in y over change in x
Example calculations for the 2 Lines Intersection Calculator
2 Lines Intersection Calculator Video
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