Question

Find the equation of the line that is perpendicular to y = 2x + 8

A) y =
1
2
x – 4
B) y = –
1
2
x – 4
C) y = 2x + 12
D) y = –2x + 12

Answer 1

`\boxed {\boxed {\sf B. \ y= - (1)/(2) x-4}}`

Explanation:

We are given the line y=2x+8. It is in slope-intercept form or y= mx+b, where m is the slope and b is the y-intercept.

The slope of the line is 2.

We want to find the equation that is perpendicular. Perpendicular lines have negative reciprocal slopes.

1. Negate

• Negate the slope, or switch the sign
• (+) 2 --> -2

2. Reciprocal

• Flip the numerator and denominator of the slope.

• -2/1 --> -1/2

The perpendicular slope is -1/2, so the correct equation must be B.