Question

write an equation in slope - intercept form of the line that passes through the points.

Explanation:

Step1: Find 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 \((x_1, y_1)=(-3, 6)\) and \((x_2, y_2)=(-1, 2)\). Then \(m=\frac{2 - 6}{-1 - (-3)}=\frac{-4}{2}=-2\).

Step2: Find the y - intercept (b)

The slope - intercept form is \(y = mx + b\). We can use one of the points, say \((0,0)\) (from the graph, the line passes through the origin) or \((-1,2)\). Let's use \((0,0)\). Substitute \(x = 0\), \(y = 0\) and \(m=-2\) into \(y=mx + b\): \(0=-2(0)+b\), so \(b = 0\).

Step3: Write the equation

Using \(m=-2\) and \(b = 0\) in the slope - intercept form \(y=mx + b\), we get \(y=-2x+0\) or \(y=-2x\).

Answer:

\(y = - 2x\)