and Generate Practice Problem Practice Problem

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Are 3x + 8y = 10 and 5x + 5y = 18:

parallel, intersect, or perpendicular

Get Eq. 1 into y = mx + b format:

3x + 8y = 10

8y = -3x + 10

Divide each side by 8

Simplifying, we have:

y = -0.375x + 1.25

Final Answer

Get Eq. 2 into y = mx + b format:

5x + 5y = 18

5y = -5x + 18

Divide each side by 5

Simplifying, we have:

y = -1x + 3.6

Final Answer

Set EQ1 = EQ2:

-0.375x + 1.25 = -1x + 3.6

-0.375x - -1x = 3.6 - 1.25

+ 0.625x = 2.35

x = 2.35/ + 0.625

x = 3.76

Plug x into equation 1

y = -0.375 * (3.76) + 1.25

y = -1.41 + 1.25

y = -0.16

Our intersection point = (3.76, -0.16)

Calculate the product of the 2 slopes:

Slope 1 * Slope 2 = -0.375 * -1 = 0.375

Perpendicular Check

Since the product of the 2 slopes ≠ -1
The lines are not perpendicular

Line Relation Check

The 2 lines intersect at (3.76, -0.16)

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) = -0.45454545454545

θ = -24.444