Question

write the equation of the line in slope - intercept form, $y = mx + b$.

Explanation:

Step1: Find two points on the line

From the graph, we can see two points \((0, - 2)\) and \((1,1)\)

Step2: Calculate the slope \(m\)

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

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

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

Step4: Write the equation in slope - intercept form

Substitute \(m = 3\) and \(b=-2\) into \(y=mx + b\). We get \(y = 3x-2\)

Answer:

\(y = 3x-2\)