Question

Question was provided via image upload.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((-1, 0)\) and \((0, 2)\).

Step2: Calculate the slope \(m\)

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

Step3: Determine the y - intercept \(b\)

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,2)\), we know that \(b = 2\).

Step4: Write the equation of the line

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m = 2\) and \(b = 2\), we get \(y=2x + 2\).

Answer:

The equation of the line is \(y = 2x+2\)