Question

write an equation of the line below.

Explanation:

Step1: Identify two points

From the graph, the two points are \((0, 2)\) (y - intercept) and \((2, -4)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 0,y_1 = 2,x_2=2,y_2=-4\), we get \(m=\frac{-4 - 2}{2 - 0}=\frac{-6}{2}=- 3\).

Step3: Use 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 \(m=-3\) and from the point \((0,2)\), \(b = 2\). So the equation of the line is \(y=-3x + 2\).

Answer:

\(y=-3x + 2\)