Are 4x + 5y = 10 and 2x + 8y = 19:
parallel, intersect, or perpendicular
Get Eq. 1 into y = mx + b format:
4x + 5y = 10
5y = -4x + 10
Divide each side by 5
| 5y |
| 5 |
| = |
| -4x + 10 |
| 5 |
Simplifying, we have:
y = -0.8x + 2
Final Answer
You have 2 free calculationss remaining
Get Eq. 2 into y = mx + b format:
2x + 8y = 19
8y = -2x + 19
Divide each side by 8
| 8y |
| 8 |
| = |
| -2x + 19 |
| 8 |
Simplifying, we have:
y = -0.25x + 2.375
Final Answer
You have 2 free calculationss remaining
Set EQ1 = EQ2:
-0.8x + 2 = -0.25x + 2.375
-0.8x - -0.25x = 2.375 - 2
- 0.55x = 0.375
x = 0.375/ - 0.55
x = -0.68181818181818
Plug x into equation 1
y = -0.8 * (-0.68181818181818) + 2
y = 0.54545454545455 + 2
y = 2.5455
Our intersection point = (-0.68181818181818, 2.5455)
Calculate the product of the 2 slopes:
Slope 1 * Slope 2 = -0.8 * -0.25 = 0.2
Perpendicular Check
Since the product of the 2 slopes ≠ -1
The lines are not perpendicular
Line Relation Check
The 2 lines intersect at (-0.68181818181818, 2.5455)
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) = | -0.25 --0.8 |
| 1 + -0.25 *-0.8 |
| tan(θ) = | 0.55 |
| 1 + 0.2 |
| tan(θ) = | 0.55 |
| 1.2 |
tan(θ) = 0.45833333333333
θ = 24.6236
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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