Question

Question was provided via image upload.

Explanation:

Step1: Identify two points on the line

From the graph, we can see two points: \((0, 2)\) (the y - intercept) and \((2, - 6)\).

Step2: Calculate the slope \(m\)

The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 0,y_1=2,x_2 = 2,y_2=-6\) into the formula:
\(m=\frac{-6 - 2}{2-0}=\frac{-8}{2}=- 4\)

Step3: Use the slope - intercept form \(y=mx + b\)

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know that \(m=-4\) and \(b = 2\) (from the point \((0,2)\)). So the equation of the line is \(y=-4x + 2\)

Answer:

The equation of the line is \(y=-4x + 2\)