Question

a line passes through the points (-5, 9) and (15, -3). 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, \( (x_1, y_1)=(-5, 9) \) and \( (x_2, y_2)=(15, - 3) \). So, \( m=\frac{-3 - 9}{15-(-5)}=\frac{-12}{20}=-\frac{3}{5} \).

Step2: Use point - slope form to find the equation

The point - slope form is \( y - y_1=m(x - x_1) \). Using the point \( (-5, 9) \) and \( m =-\frac{3}{5} \), we have \( y - 9=-\frac{3}{5}(x + 5) \).

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y-9 =-\frac{3}{5}x-3 \). Then add 9 to both sides: \( y=-\frac{3}{5}x-3 + 9 \), so \( y=-\frac{3}{5}x + 6 \).

Answer:

\( y =-\frac{3}{5}x+6 \)