Chapter 3.4, Problem 33PPS

To determine

To write an equation of line through $(-1,-2)$ and $(3,4)$ in slope intercept form.

Answer to Problem 33PPS

Slope intercept form

  $y=\frac{3}{2}x-\frac{1}{2}$

Explanation of Solution

Given information:

Line through $(-1,-2)$ and $(3,4)$

Formula used:

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

Point-slope form

  $y-y_1=m(x-x_1)$

Slope intercept form

  $y=mx+b$

Calculation:

Points

$(-1,-2)$ and $(3,4)$

Here

  $x_1=-1$

  $y_1=-2$

  $x_2=3$

  $y_2=4$

Using slope formula to calculate slope of line

  $m=\frac{4-(-2)}{3-(-1)}$

On solving

  $m=\frac{6}{4}$

On solving

  $m=\frac{3}{2}$

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

  $m=\frac{3}{2}$

Let take point $(3,4)$

Here

  $x_1=3$

  $y_1=4$

Point-slope form

  $y-4=\frac{3}{2}(x-3)$

On solving

  $y-4=\frac{3}{2}x-\frac{9}{2}$

Add 4 both sides

  $y-4+4=\frac{3}{2}x-\frac{9}{2}+4$

On solving

  $y=\frac{3}{2}x-\frac{1}{2}$

Hence, slope intercept form is $y=\frac{3}{2}x-\frac{1}{2}$