Chapter 1, Problem 27RE

To determine

To find: an equation of the line

Answer to Problem 27RE

Theequation of the line is $y=-2x+5$

Explanation of Solution

Given:

Slope =-2

point (3,-1)

Calculation:

An equation of a no vertical line with slope $m$ that contains the point $\left(x_1,y_1\right)$ is

  $y-y_1=m\left(x-x_1\right)$

So, the equation of the line having the point (3,-1) and slope $m=-2$ can be determined.

  $y-(-1)=-2(x-3)y+1=-2x+6$

Subtract 1 from both sides of the equation.

  $y+1-1=-2x+6-1y=-2x+5$

Therefore, the equation of the line is $y=-2x+5$

Conclusion:

Therefore, the equation of the line is $y=-2x+5$