Question

Determine if the two lines are perpendicular. Explain how you know by calculating the slopes and comparing the slopes in 2-3 sentences.

Answer 1

Answer:

The two lines are not perpendicular because the product of their slopes is not equal to -1

Step-by-step explanation:

The product of the slopes of the perpendicular line is -1

• That means one of them is and additive and multiplicative inverse of the other

• If the slope of one of them is m, then reciprocal m and change its sign, then the slope of the perpendicular is $-\frac{1}{m}$
• The formula of the slope is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Let us find from the graph two points lie on each line and calculate the slopes of them and then find its product if the product is -1, then the two lines are perpendicular

From the graph

∵ The red line passes through points (4 , 0) and (0 , 8)

∴ $x_{1}$ = 4 and $x_{2}$ = 0

∴ $y_{1}$ = 0 and $y_{2}$ = 8

∵ $m=\frac{8-0}{0-4}=\frac{8}{-4}=-2$

∴ The slope of the red line is -2

∵ The blue line passes through points (5 , 5) and (0 , -5)

∴ $x_{1}$ = 5 and $x_{2}$ = 0

∴ $y_{1}$ = 5 and $y_{2}$ = -5

∵ $m=\frac{-5-5}{0-5}=\frac{-10}{-5}=2$

∴ The slope of the blue line is 2

∵ The products of the slopes of the two lines = -2 × 2 = -4

∴ The product of the slopes of the lines not equal -1

∴ The two lines are not perpendicular