Question

what is the equation of the following line?

Explanation:

Step1: Identify two points on the line

From the graph, the line passes through \((0, -3)\) (the y - intercept) and \((6, 0)\) (the x - intercept).

Step2: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 3)\) and \((x_2,y_2)=(6,0)\). Then \(m=\frac{0 - (-3)}{6 - 0}=\frac{3}{6}=\frac{1}{2}\).

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 \(m = \frac{1}{2}\) and from the point \((0,-3)\), \(b=-3\). So the equation of the line is \(y=\frac{1}{2}x-3\).

Answer:

\(y=\frac{1}{2}x - 3\)