Chapter 4, Problem 5CT

To determine

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

Answer to Problem 5CT

The equation of the line is $y=3x-2.$

Explanation of Solution

Given information:

The line is parallel to line $y=3x-1$ and passes through (-2,-8).

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 $y=3x-1$ is 3.

Since all parallel lines have the same slope so 3 is also the slope of the line parallel to line $y=3x-1$ .

  $m=3$ .

Substituting $m=3.$ in equation (1),

  $y=3x+b.$ ….2

Since line passes through (-2,-8) so substituting -2 for $x$ and -8 for $y$ in equation (2).

  $\begin{array}{c}-8=3\times (-2)+b.\\ -8=-6+b.\\ b=-8+6.\\ b=-2.\end{array}$

The equation of the line in slope-intercept formhas slop of 3 and y-intercept is -2is, $y=3x-2.$