Question

graph the line that passes through the points (-6, 2) and (-8, 1) and determine the equation of the line.

Explanation:

Step1: Calculate the slope

The formula for slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let \((x_1, y_1)=(-6, 2)\) and \((x_2, y_2)=(-8, 1)\). Then \( m=\frac{1 - 2}{-8 - (-6)}=\frac{-1}{-2}=\frac{1}{2} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((-6, 2)\) and \( m = \frac{1}{2} \), we have \( y - 2=\frac{1}{2}(x + 6) \).

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y - 2=\frac{1}{2}x+3 \). Then add 2 to both sides: \( y=\frac{1}{2}x + 5 \).

Answer:

The equation of the line is \( y=\frac{1}{2}x + 5 \)