Are 2x + 2y = 11 and 2x + 4y = 12:
parallel, intersect, or perpendicular
Get Eq. 1 into y = mx + b format:
2x + 2y = 11
2y = -2x + 11
Divide each side by 2
| 2y |
| 2 |
| = |
| -2x + 11 |
| 2 |
Simplifying, we have:
y = -1x + 5.5
Final Answer
Slope = -1
Get Eq. 2 into y = mx + b format:
2x + 4y = 12
4y = -2x + 12
Divide each side by 4
| 4y |
| 4 |
| = |
| -2x + 12 |
| 4 |
Simplifying, we have:
y = -0.5x + 3
Final Answer
Slope = -0.5
Set EQ1 = EQ2:
-1x + 5.5 = -0.5x + 3
-1x - -0.5x = 3 - 5.5
- 0.5x = -2.5
x = -2.5/ - 0.5
x = 5
Plug x into equation 1
y = -1 * (5) + 5.5
y = -5 + 5.5
y = 0.5
Our intersection point = (5, 0.5)
Calculate the product of the 2 slopes:
Slope 1 * Slope 2 = -1 * -0.5 = 0.5
Perpendicular Check
Since the product of the 2 slopes ≠ -1
The lines are not perpendicular
Line Relation Check
The 2 lines intersect at (5, 0.5)
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) = | -0.5 --1 |
| 1 + -0.5 *-1 |
| tan(θ) = | 0.5 |
| 1 + 0.5 |
| tan(θ) = | 0.5 |
| 1.5 |
tan(θ) = 0.33333333333333
θ = 18.4349
