Are 6x + 5y = 15 and 8x + 5y = 11:
parallel, intersect, or perpendicular
Get Eq. 1 into y = mx + b format:
6x + 5y = 15
5y = -6x + 15
Divide each side by 5
| 5y |
| 5 |
| = |
| -6x + 15 |
| 5 |
Simplifying, we have:
y = -1.2x + 3
Final Answer
Slope = -1.2
Get Eq. 2 into y = mx + b format:
8x + 5y = 11
5y = -8x + 11
Divide each side by 5
| 5y |
| 5 |
| = |
| -8x + 11 |
| 5 |
Simplifying, we have:
y = -1.6x + 2.2
Final Answer
Slope = -1.6
Set EQ1 = EQ2:
-1.2x + 3 = -1.6x + 2.2
-1.2x - -1.6x = 2.2 - 3
+ 0.4x = -0.8
x = -0.8/ + 0.4
x = -2
Plug x into equation 1
y = -1.2 * (-2) + 3
y = 2.4 + 3
y = 5.4
Our intersection point = (-2, 5.4)
Calculate the product of the 2 slopes:
Slope 1 * Slope 2 = -1.2 * -1.6 = 1.92
Perpendicular Check
Since the product of the 2 slopes ≠ -1
The lines are not perpendicular
Line Relation Check
The 2 lines intersect at (-2, 5.4)
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) = | -1.6 --1.2 |
| 1 + -1.6 *-1.2 |
| tan(θ) = | -0.4 |
| 1 + 1.92 |
| tan(θ) = | -0.4 |
| 2.92 |
tan(θ) = -0.13698630136986
θ = -7.8002
