Question

graph the line that passes through the points (3, -6) and (9, -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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1, y_1)=(3, - 6)\) and \((x_2, y_2)=(9, - 2)\). So, \( m=\frac{-2-(-6)}{9 - 3}=\frac{-2 + 6}{6}=\frac{4}{6}=\frac{2}{3} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((3,-6)\) and \( m = \frac{2}{3} \), we have \( y-(-6)=\frac{2}{3}(x - 3) \).
Simplify the equation:
\( y + 6=\frac{2}{3}x-2 \)
Subtract 6 from both sides: \( y=\frac{2}{3}x-2 - 6 \), so \( y=\frac{2}{3}x-8 \).

Answer:

The equation of the line is \( y=\frac{2}{3}x - 8 \)