Chapter 3.4, Problem 8CYU

To determine

To write an equation of line through $(4,3)$ and $(1,-6)$ in point-slope form.

Answer to Problem 8CYU

Slope intercept form

  $y=\frac{1}{3}x+\frac{5}{3}$

Explanation of Solution

Given information:

Line through $(4,3)$ and $(1,-6)$

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

  $(4,3)$

  $(1,-6)$

Here

  $x_1=4$

  $y_1=3$

  $x_2=1$

  $y_2=-6$

Using slope formula to calculate slope of line

  $m=\frac{\text{ 1}-4}{-6-3}$

On solving

  $m=\frac{-3}{-9}$

On solving

  $m=\frac{1}{3}$

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

  $m=\frac{\text{ 3}}{5}$

Let take point $(4,3)$

Here

  $x_1=4$

  $y_1=3$

Point-slope form

  $y-3=\frac{1}{3}(x-4)$

On solving

  $y-3=\frac{1}{3}x-\frac{4}{3}$

Add 3 both sides

  $y-3+3=\frac{1}{3}x-\frac{4}{3}+3$

On solving

  $y=\frac{1}{3}x+\frac{5}{3}$

Hence, slope intercept form is $y=\frac{1}{3}x+\frac{5}{3}$