Question

Determine whether the slope of the two lines are parallel, perpendicular, or neither:

H(-4,0) U(0,3); L(-4,-3) K(8,6)
O Parallel
O Perpendicular
O Neither

Answer 1

Parallel

Explanation:

`\boxed{\begin{minipage}{4 cm}\underline{Slope formula}\\\\slope ($m$) $=(y_2-y_1)/(x_2-x_1)$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\end{minipage}}`

Define the points for line HU:

• (x₁, y₁) = H = (-4, 0)
• (x₂, y₂) = J = (0, 3)

Substitute the defined points into the slope formula:

`\implies \textsf{slope}=(y_2-y_1)/(x_2-x_1)=(3-0)/(0-(-4))=(3)/(4)`

Define the points for line LK:

• (x₁, y₁) = L = (-4, -3)
• (x₂, y₂) = K = (8, 6)

Substitute the defined points into the slope formula:

`\implies \textsf{slope}=(y_2-y_1)/(x_2-x_1)=(6-(-3))/(8-(-4))=(9)/(12)=(3)/(4)`

If two lines are parallel, the slopes are the same.

If two lines are perpendicular, the slopes are negative reciprocals.

Therefore, as the slopes of the two lines are the same, the lines are parallel.