Are 8x + 6y = 19 and 5x + 6y = 12:
parallel, intersect, or perpendicular
Get Eq. 1 into y = mx + b format:
8x + 6y = 19
6y = -8x + 19
Divide each side by 6
| 6y |
| 6 |
| = |
| -8x + 19 |
| 6 |
Simplifying, we have:
y = -1.3333333333333x + 3.1666666666667
Final Answer
Get Eq. 2 into y = mx + b format:
5x + 6y = 12
6y = -5x + 12
Divide each side by 6
| 6y |
| 6 |
| = |
| -5x + 12 |
| 6 |
Simplifying, we have:
y = -0.83333333333333x + 2
Final Answer
Set EQ1 = EQ2:
-1.3333333333333x + 3.1666666666667 = -0.83333333333333x + 2
-1.3333333333333x - -0.83333333333333x = 2 - 3.1666666666667
- 0.5x = -1.1666666666667
x = -1.1666666666667/ - 0.5
x = 2.3333333333333
Plug x into equation 1
y = -1.3333333333333 * (2.3333333333333) + 3.1666666666667
y = -3.1111111111111 + 3.1666666666667
y = 0.0556
Our intersection point = (2.3333333333333, 0.0556)
Calculate the product of the 2 slopes:
Slope 1 * Slope 2 = -1.3333333333333 * -0.83333333333333 = 1.1111111111111
Perpendicular Check
Since the product of the 2 slopes ≠ -1
The lines are not perpendicular
Line Relation Check
The 2 lines intersect at (2.3333333333333, 0.0556)
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) = | -0.83333333333333 --1.3333333333333 |
| 1 + -0.83333333333333 *-1.3333333333333 |
| tan(θ) = | 0.5 |
| 1 + 1.1111111111111 |
| tan(θ) = | 0.5 |
| 2.1111111111111 |
tan(θ) = 0.23684210526316
θ = 13.3245
Keep Practicing
Common Core State Standards In This Lesson
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
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