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Chapter 3: Q 3.62. (page 288)

Find an equation of a line perpendicular to the line y=12x-3that contains the point (6,4). Write the equation in slope-intercept form.

Short Answer

Expert verified

The equation isy=-2x+16

Step by step solution

01

Step 1. Find the slope of the given line

The given line is:

y=12x-3

The line is in slope-intercept form. Therefore, its slope is:

m=12

02

Step 2. Find the slope of the perpendicular line and identify the point

The slopes of perpendicular lines are negative reciprocals.

Therefore, the slope of the perpendicular line is:

m1=-2

And the given point is (6,4).

(x1,y1)=(6,4)

03

Step 3. Substitute the values into the point-slope form

The point-slope form is:

y-y1=m(x-x1)y-4=-2(x-6)y-4=-2x+12

04

Step 4. Write the equation in slope-intercept form

The slope-intercept form of the perpendicular line isy=-2x+16.

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Most popular questions from this chapter

Determine whether each equation is a function.

  1. x+y2=4
  2. y=x2-7
  3. y=5x-4

Graph the equationsx=-2,y=-5.

Graph the equationsx=4andy=3.

Find the equation of the line shown in each graph and write the equation in slope-intercept form.

In the following exercises, graph each function state its domain and range. Write the domain and range in interval notation.

f(x)=x+2
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