Chapter 3.4, Problem 22PPS

To determine

To write in slope intercept form for the line that having slope $\frac{5}{7}$ and containing $(-2,-5)$ .Then graph the line.

Answer to Problem 22PPS

Line

  $y=\frac{5}{7}x-\frac{25}{7}$

Graph

Explanation of Solution

Given information:

The line having slope and point

  $m=\frac{5}{7}$

  $(-2,-5)$

Formula used:

Point-slope form

  $y-y_1=m(x-x_1\text{)}$

Calculation:

The line having slope and point

  $m=\frac{5}{7}$

  $(-2,-5)$

Here

  $x_1=-2$

  $y_1=-5$

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

  $y-(-5)=\frac{5}{7}(x-(-2)\text{) }$

On solving

  $y+5=\frac{5}{7}(x+2)$

On solving

  $y+5=\frac{5}{7}x+\frac{10}{7}$

Subtract $5$ both sides

  $y+5-5=\frac{5}{7}x+\frac{10}{7}-5$

On solving

  $y=\frac{5}{7}x-\frac{25}{7}$

Substituting $x=0$

Then

  $y=-\frac{25}{7}$

Substituting $y=0$

Then

  $0=\frac{5}{7}x-\frac{25}{7}$

On solving

  $\frac{5}{7}x=\frac{25}{7}$

On solving

  $x=5$

Table

Then graph