Question

What is an equation of the line that passes through the points (6, 8) and (−3,2)?

Answer 1

Explanation

• Calculate the slope by using rise over run with two given coordinate points.

$m = \frac{8 - 2}{6 - ( - 3)} \\ m = \frac{6}{6 + 3} \\ m = \frac{6}{9} \\ m = \frac{2}{3}$

The slope is 2/3.

• Slope-intercept form

$y = mx + b$

where m = slope and b = y-intercept. Substitute the value of m in slope-intercept form.

$y = \frac{2}{3} x + b$

• Substitute one of two coordinate points in the slope-intercept form.

I will use (-3,2) instead.

$2 = \frac{2}{3} ( - 3) + b \\ 2 = - 2 + b \\ 2 + 2 = b \\ 4 = b$

The y-intercept is (0,4). Then rewrite the equation by substituting the b-value and slope in slope-intercept form.

$y = \frac{2}{3} x + 4$

Answer

$\large \boxed{y = \frac{2}{3} x + 4}$