Chapter 3.4, Problem 3ACYP

To determine

To write an equation of line through $(-2,4)$ and $(8,10)$ in point-slope form.

Answer to Problem 3ACYP

Slope intercept form

  $y=\frac{3}{5}x+\frac{26}{5}$

Explanation of Solution

Given information:

Line through $(-2,4)$ and $(8,10)$

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

  $(-2,4)$

  $(8,10)$

Here

  $x_1=-2$

  $y_1=4$

  $x_2=8$

  $y_2=10$

Using slope formula to calculate slope of line

  $m=\frac{\text{ 10}-4}{8-(-2)}$

On solving

  $m=\frac{\text{ 6}}{10}$

On solving

  $m=\frac{\text{ 3}}{5}$

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

  $m=\frac{\text{ 3}}{5}$

Let take point $(-2,4)$

Here

  $x_1=-2$

  $y_1=4$

Point-slope form

  $y-4=\frac{3}{5}(x-(-2))$

On solving

  $y-4=\frac{3}{5}(x+2)$

On solving

  $y-4=\frac{3}{5}x+\frac{6}{5}$

Add 4 both sides

  $y-4+4=\frac{3}{5}x+\frac{6}{5}+4$

On solving

  $y=\frac{3}{5}x+\frac{26}{5}$

Hence, slope intercept form is $y=\frac{3}{5}x+\frac{26}{5}$