Question

find the equation of the line passing through the points (4, -6) and (0, 8).

Explanation:

Step1: Identify slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$.

Step2: Calculate the slope

Let $(x_1,y_1)=(4,-6)$ and $(x_2,y_2)=(0,8)$.
$m=\frac{8-(-6)}{0-4}=\frac{14}{-4}=-\frac{7}{2}$

Step3: Identify y-intercept

The point $(0,8)$ is the y-intercept, so $b=8$.

Step4: Write line equation

Use slope-intercept form $y=mx+b$.
$y=-\frac{7}{2}x+8$

Answer:

$y=-\frac{7}{2}x+8$