Chapter 3.4, Problem 23PPS

To determine

To write in slope intercept form for the line that having slope $-\frac{4}{5}$ and containing $(-3,-6)$ .Then graph the line.

Answer to Problem 23PPS

Line

  $y=\frac{-4}{5}x-\frac{42}{5}$

Graph

Explanation of Solution

Given information:

The line having slope and point

  $m=\frac{-4}{5}$

  $(-3,-6)$

Formula used:

Point-slope form

  $y-y_1=m(x-x_1\text{)}$

Calculation:

The line having slope and point

  $m=\frac{-4}{5}$

  $(-3,-6)$

Here

  $x_1=-3$

  $y_1=-6$

Substitute value of slope and point in the point-slope form

  $y-(-6)=\frac{-4}{5}(x-(-3)\text{) }$

On solving

  $y+6=\frac{-4}{5}(x+3\text{) }$

On solving

  $y+6=\frac{-4}{5}x-\frac{12}{5}$

Subtract $6$ both sides

  $y+6-6=\frac{-4}{5}x-\frac{12}{5}-6$

On solving

  $y=\frac{-4}{5}x-\frac{42}{5}$

Substituting $x=0$

Then

  $y=-\frac{42}{5}$

Substituting $y=0$

Then

  $0=\frac{-4}{5}x-\frac{42}{5}$

On solving

  $\frac{4}{5}x=-\frac{42}{5}$

On solving

  $x=-\frac{21}{2}$

Table

Then graph