Chapter 3.4, Problem 7CYU

To determine

To write an equation of line through $(0,-1)$ and $(4,4)$ in point-slope form.

Answer to Problem 7CYU

Slope intercept form

  $y=\frac{4}{5}x-1$

Explanation of Solution

Given information:

Line through $(0,-1)$ and $(4,4)$

Formula used:

Slope, $m=\frac{y_2-y_1}{x_2-x_1}$

Point-slope form

  $y-y_1=m(x-x_1)$

Calculation:

Points

  $(0,-1)$

  $(4,4)$

Here

  $x_1=0$

  $y_1=-1$

  $x_2=4$

  $y_2=4$

Using slope formula to calculate slope of line

  $m=\frac{\text{ 4}-0}{4-(-1)}$

On solving

  $m=\frac{\text{ 4}}{5}$

Using slope and any one of the point to find slope intercept form

  $m=\frac{\text{ 4}}{5}$

Let take point $(0,-1)$

Here

  $x_1=0$

  $y_1=-1$

Point-slope form

  $y-(-1)=\frac{4}{5}(x-0)$

On solving

  $y+1=\frac{4}{5}x$

Subtract 1 both sides

  $y+1-1=\frac{4}{5}x-1$

On solving

  $y=\frac{4}{5}x-1$

Hence, slope intercept form is $y=\frac{4}{5}x-1$