Question

Write an equation of the line that passes through the point (8, -1) and is perpendicular to the line pictured.

A)
y = 4x


B)
y = 4x + 1


C)
y = -
1
4
x


D)
y = -
1
4
x + 1

Answer 1

D y = -¼x + 1

Explanation:

y-intercept = 0

Slope: (4-0)/(1-0) = 4

y = 4x + 0

y = 4x

Slope of the Perpendicular line:

-¼

Using (8,-1)

y - (-1) = -¼(x - 8)

y + 1= -¼x + 2

y = -¼x + 1

Answer 2

y = -1/4x+1

Explanation:

First we need to find the slope of the line pictured

(1,4) and (0,0)

m = (y2-y1)/(x2-x1)

= (0-4)/(0-1)

= -4/-1

=4

The perpendicular line has a slope that is the negative reciprocal

-1 /(4)

-1/4

We have a point and a line

y = mx+b where m is the slope and b is the y intercept

y = -1/4x +b

-1 = -1/4(8) +b

-1 = -2+b

Add 2 to each side

b = 1

y = -1/4x+1