Question

1. write the equation of the line shown.

Explanation:

Step1: Identify two points

From the graph, two points on the line are \((-3, 0)\) and \((0, 3)\) (the y - intercept).

Step2: Calculate the slope \(m\)

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

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

Answer:

\(y=x + 3\)