Question

write an equation of the line below.

Explanation:

Step1: Identify two points

From the graph, the two points are \((0, -1)\) (the y - intercept) and \((2, 7)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 1)\) and \((x_2,y_2)=(2,7)\). Then \(m=\frac{7-(-1)}{2 - 0}=\frac{8}{2}=4\).

Step3: Use slope - intercept form

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know \(m = 4\) and \(b=-1\) (from the point \((0,-1)\)). So the equation is \(y = 4x-1\).

Answer:

\(y = 4x-1\)