Question

a line passes through the points (-3, 8) and (2, -2). write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( (x_1, y_1)=(-3, 8) \) and \( (x_2, y_2)=(2, -2) \). So, \( m=\frac{-2 - 8}{2 - (-3)}=\frac{-10}{5}=-2 \).

Step2: Use point - slope form to find the equation

The point - slope form is \( y - y_1=m(x - x_1) \). Using the point \( (-3, 8) \) and \( m = - 2 \), we have \( y - 8=-2(x + 3) \).

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y - 8=-2x-6 \). Then, add 8 to both sides: \( y=-2x + 2 \).

Answer:

\( y=-2x + 2 \)