Question

write an equation of the line below.

Explanation:

Step1: Identify two points

From the graph, we can see two points: \((0, 4)\) (the y - intercept) and \((-5, 6)\) (the other marked point).

Step2: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,4)\) and \((x_2,y_2)=(-5,6)\). Then \(m=\frac{6 - 4}{-5-0}=\frac{2}{-5}=-\frac{2}{5}\).

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 \(m =-\frac{2}{5}\) and \(b = 4\) (since the line crosses the y - axis at \((0,4)\)). So the equation of the line is \(y=-\frac{2}{5}x + 4\).

Answer:

\(y =-\frac{2}{5}x + 4\)