Question

graph the line that passes through the points $(-3, -9)$ and $(6, 3)$ and determine the equation of the line.

Explanation:

Step1: Calculate the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1)=(-3, -9)\) and \((x_2, y_2)=(6, 3)\). Then \(m=\frac{3 - (-9)}{6 - (-3)}=\frac{12}{9}=\frac{4}{3}\).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \(y - y_1=m(x - x_1)\). We can use the point \((6, 3)\) (we could also use \((-3,-9)\)). Substitute \(m = \frac{4}{3}\), \(x_1 = 6\) and \(y_1 = 3\) into the formula:
\(y - 3=\frac{4}{3}(x - 6)\)

Step3: Simplify the equation to slope - intercept form (\(y=mx + b\))

Expand the right - hand side: \(y-3=\frac{4}{3}x-8\)
Add 3 to both sides: \(y=\frac{4}{3}x-8 + 3\), so \(y=\frac{4}{3}x-5\)

Answer:

The equation of the line is \(y=\frac{4}{3}x - 5\)