Question

write an equation of the line below.

Explanation:

Step1: Identify two points on the line

From the graph, we can see two points: \((0, 1)\) (the y - intercept) and \((5, 4)\).

Step2: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,1)\) and \((x_2,y_2)=(5,4)\). Then \(m = \frac{4 - 1}{5 - 0}=\frac{3}{5}\).

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 \(m=\frac{3}{5}\) and from the point \((0,1)\), the y - intercept \(b = 1\). So the equation of the line is \(y=\frac{3}{5}x+1\).

Answer:

\(y=\frac{3}{5}x + 1\)