Question

the equation of the line is:

Explanation:

Step1: Find two points on the line

Let's take two points \((x_1,y_1)=(-1,0)\) and \((x_2,y_2)=(0,2)\) from the graph.

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the values, we get \(m=\frac{2 - 0}{0-(-1)}=\frac{2}{1}=2\).

Step3: Use the slope - intercept form \(y = mx + b\)

The \(y\) - intercept \(b\) is the \(y\) - value when \(x = 0\). From the point \((0,2)\), \(b = 2\). Since \(m = 2\) and \(b=2\), the equation of the line is \(y=2x + 2\).

Answer:

\(y = 2x+2\)