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Chapter 3: Q. 225 (page 294)

Find the equation of the line that has the slope m=-34, containing the point(8,-5). Write the equation in the slope-intercept form.

Short Answer

Expert verified

The equation of the line in the slope-intercept form isy=-34x+1

Step by step solution

01

Step 1. Given Information

The slope of the line is m=-34and the point on it is (8,-5)

We will use the slope-point formula to find the equation of the line.

02

Step 2. Formula

  • The slope-intercept form of the equation of the line is y=mx+bwhere mis the slope and bis the y-intercept.
  • The point-slope form can be given asy-y1=m(x-x1)wheremis the slope and(x1,y1)is a point on the line.
03

Step 3. Finding the equation of the line

We have the slope, m=-34and the point x1,y1=(8,-5)

Using the slope-point form, we have

y-y1=m(x-x1)y-(-5)=-34(x-8)y+5=-34x+244y=-34x+6-5y=-34x+1

Therefore the equation of the line in the slope-intercept form isy=-34x+1

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