Question

write an equation of the line below.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, -1)\) (the y - intercept) and \((3, -7)\).

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 \((x_2,y_2)=(3, -7)\). Then \(m=\frac{-7-(-1)}{3 - 0}=\frac{-7 + 1}{3}=\frac{-6}{3}=-2\).

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 \(m=-2\) and from the point \((0,-1)\), \(b=-1\) (since when \(x = 0\), \(y=b\)). So the equation of the line is \(y=-2x-1\).

Answer:

\(y = - 2x-1\)