Question

a line passes through the points (-2, 6) and (1, -9). 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, \( x_1=-2,y_1 = 6,x_2=1,y_2=-9 \). So \( m=\frac{-9 - 6}{1-(-2)}=\frac{-15}{3}=- 5 \).

Step2: Use point - slope form to find the equation

The point - slope form is \( y - y_1=m(x - x_1) \). Using the point \((-2,6)\) and \( m=-5 \), we have \( y - 6=-5(x + 2) \).

Step3: Convert to slope - intercept form (\(y=mx + b\))

Expand the right - hand side: \( y-6=-5x-10 \). Then add 6 to both sides: \( y=-5x-10 + 6=-5x-4 \).

Answer:

\( y=-5x - 4 \)