Are 2x+8y=20 and 3x+9y=50:
parallel, intersect, or perpendicular
Get Eq. 1 into y = mx + b format:
2x + 8y = 20
8y = -2x + 20
Divide each side by 8
| 8y |
| 8 |
| = |
| -2x + 20 |
| 8 |
Simplifying, we have:
y = -0.25x + 2.5
Final Answer
Get Eq. 2 into y = mx + b format:
3x + 9y = 50
9y = -3x + 50
Divide each side by 9
| 9y |
| 9 |
| = |
| -3x + 50 |
| 9 |
Simplifying, we have:
y = -0.33333333333333x + 5.5555555555556
Final Answer
Set EQ1 = EQ2:
-0.25x + 2.5 = -0.33333333333333x + 5.5555555555556
-0.25x - -0.33333333333333x = 5.5555555555556 - 2.5
+ 0.083333333333333x = 3.0555555555556
x = 3.0555555555556/ + 0.083333333333333
x = 36.666666666667
Plug x into equation 1
y = -0.25 * (36.666666666667) + 2.5
y = -9.1666666666667 + 2.5
y = -6.6667
Our intersection point = (36.666666666667, -6.6667)
Calculate the product of the 2 slopes:
Slope 1 * Slope 2 = -0.25 * -0.33333333333333 = 0.083333333333333
Perpendicular Check
Since the product of the 2 slopes ≠ -1
The lines are not perpendicular
Line Relation Check
The 2 lines intersect at (36.666666666667, -6.6667)
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) = | -0.33333333333333 --0.25 |
| 1 + -0.33333333333333 *-0.25 |
| tan(θ) = | -0.083333333333333 |
| 1 + 0.083333333333333 |
| tan(θ) = | -0.083333333333333 |
| 1.0833333333333 |
tan(θ) = -0.076923076923077
θ = -4.3987
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
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
