Chapter 3.4, Problem 30PPS

To determine

To write an equation of line through $(2,4)$ and $(-4,-11)$ in slope intercept form.

Answer to Problem 30PPS

Slope intercept form

  $y=\frac{15}{6}x-1$

Explanation of Solution

Given information:

Line through $(2,4)$ and $(-4,-11)$

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

$(2,4)$ and $(-4,-11)$

Here

  $x_1=2$

  $y_1=4$

  $x_2=-4$

  $y_2=-11$

Using slope formula to calculate slope of line

  $m=\frac{-11-4}{-4-2}$

On solving

  $m=\frac{-15}{-6}$

On solving

  $m=\frac{15}{6}$

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

  $m=\frac{15}{6}$

Let take point $(2,4)$

Here

  $x_1=2$

  $y_1=4$

Point-slope form

  $y-4=\frac{15}{6}(x-2)$

On solving

  $y-4=\frac{15}{6}x-5$

Add 4 both sides

  $y-4+4=\frac{15}{6}x-5+4$

On solving

  $y=\frac{15}{6}x-1$

Hence, slope intercept form is $y=\frac{15}{6}x-1$