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 \((6, - 1)\).

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

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

Answer:

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