Chapter 3.4, Problem 9CYU

To determine

To write an equation of line through $(6,5)$ and $(-1,-4)$ in point-slope form.

Answer to Problem 9CYU

Slope intercept form

  $y=\frac{9}{7}x-\frac{19}{7}$

Explanation of Solution

Given information:

Line through $(6,5)$ and $(-1,-4)$

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

  $(6,5)$

  $(-1,-4)$

Here

  $x_1=6$

  $y_1=5$

  $x_2=-1$

  $y_2=-4$

Using slope formula to calculate slope of line

  $m=\frac{-4-5}{-1-6}$

On solving

  $m=\frac{9}{7}$

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

  $m=\frac{9}{7}$

Let take point $(6,5)$

Here

  $x_1=6$

  $y_1=5$

Point-slope form

  $y-5=\frac{9}{7}(x-6)$

On solving

  $y-5=\frac{9}{7}x-\frac{54}{7}$

Add 5 both sides

  $y-5+5=\frac{9}{7}x-\frac{54}{7}+5$

On solving

  $y=\frac{9}{7}x-\frac{19}{7}$

Hence, slope intercept form is $y=\frac{9}{7}x-\frac{19}{7}$