2x=6y+5 and 6x - 3y = 18 Generate Practice Problem Practice Problem

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Are 7x + 3y = 13 and 7x + 8y = 17:

parallel, intersect, or perpendicular

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

7x + 3y = 13

3y = -7x + 13

Divide each side by 3

Simplifying, we have:

y = -2.3333333333333x + 4.3333333333333

Final Answer

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

7x + 8y = 17

8y = -7x + 17

Divide each side by 8

Simplifying, we have:

y = -0.875x + 2.125

Final Answer

Set EQ1 = EQ2:

-2.3333333333333x + 4.3333333333333 = -0.875x + 2.125

-2.3333333333333x - -0.875x = 2.125 - 4.3333333333333

- 1.4583333333333x = -2.2083333333333

x = -2.2083333333333/ - 1.4583333333333

x = 1.5142857142857

Plug x into equation 1

y = -2.3333333333333 * (1.5142857142857) + 4.3333333333333

y = -3.5333333333333 + 4.3333333333333

y = 0.8

Our intersection point = (1.5142857142857, 0.8)

Calculate the product of the 2 slopes:

Slope 1 * Slope 2 = -2.3333333333333 * -0.875 = 2.0416666666667

Perpendicular Check

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

Line Relation Check

The 2 lines intersect at (1.5142857142857, 0.8)

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) = 0.47945205479452

θ = 25.6155