Question

write an equation of the line below.

Explanation:

Step1: Identify two points on the line

From the graph, we can see two points: \((0, -4)\) (the y - intercept) and \((3, -7)\).

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 \(x_1 = 0,y_1=-4,x_2 = 3,y_2=-7\) into the formula:
\(m=\frac{-7-(-4)}{3 - 0}=\frac{-7 + 4}{3}=\frac{-3}{3}=- 1\)

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 \(m=-1\) and from the point \((0,-4)\), the y - intercept \(b=-4\).
Substituting \(m=-1\) and \(b = - 4\) into the slope - intercept form, we get \(y=-x-4\)

Answer:

\(y=-x - 4\)