Questions: Complete the sentence below. The lines y=3x-1 and y=ax+2 are perpendicular if a= . (Simplify your answer.)

Transcript text: Complete the sentence below. The lines $y=3 x-1$ and $y=a x+2$ are perpendicular if $a=$ $\square$ . (Simplify your answer.)

Solution

Step 1: Understanding the Problem

We are given two lines described by the equations $y = mx + b$ and $y = nx + c$. We need to determine if these lines are perpendicular.

Step 2: Applying the Perpendicularity Condition

Two lines are perpendicular if the product of their slopes is -1. Given the slopes $m = 3$ and $n = -0.333$, we check this condition.

Calculation

The product of the slopes is $mn = 3 \times -0.333 = -1$.

Since $mn = -1$, the lines are perpendicular.

The lines described by $y = 3x - 1$ and $y = -0.3333333333333333x + 2$ are perpendicular.

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