Question

graph the line that passes through the points (-9, 1) and (-6, -2) and determine the equation of the line.

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let \((x_1, y_1)=(-9, 1)\) and \((x_2, y_2)=(-6, -2)\). Then \( m=\frac{-2 - 1}{-6 - (-9)}=\frac{-3}{3}=-1 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((-9, 1)\) and \( m = - 1 \), we have \( y - 1=-1(x + 9) \).

Step3: Simplify to slope - intercept form

Simplify \( y - 1=-x - 9 \) to get \( y=-x - 8 \).

Answer:

The equation of the line is \( y=-x - 8 \)