Chapter 4, Problem 6CT

To determine

Write an equation of the line in slope-intercept form.

Answer to Problem 6CT

The equation of the line is $y=-4x+5.$

Explanation of Solution

Given information:

The line is perpendicular to line $y=(1/4)x-9$ and passes through (1,1).

Calculation:

Formula :

In general slope intercept equation of a line is,

  $y=mx+b$ ….1

where $m$ is the slope of the line and $b$ is the y-intercept.

The slope of line $y=(1/4)x-9$ is 1/4.

Since the slope of two perpendicular lines is negative reciprocal to each other so the slope of line perpendicular to $y=(1/4)x-9$ is negative reciprocal of 1/4 that is -4 so,

  $m=-4$ .

Substituting $m=-4$ in equation (1),

  $y=-4x+b.$ ….2

Since line passes through (1,1) so substituting 1 for $x$ and 1 for $y$ in equation (2).

  $\begin{array}{c}1=-4\times 1+b.\\ 1=-4+b.\\ b=1+4.\\ b=5.\end{array}$

The equation of the line in slope-intercept form has slop of -4 and y-intercept is 5 is, $y=-4x+5.$