Question

write the equation of the line in fully simplified slope - intercept form.

Explanation:

Step1: Identify two points on the line

Looking at the graph, we can see that the line passes through the points \((0, -2)\) (the y-intercept) and \((1, 0)\).

Step2: Calculate the slope (\(m\))

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((0, -2)\) and \((1, 0)\), we have \(m=\frac{0 - (-2)}{1 - 0}=\frac{2}{1} = 2\).

Step3: Write the equation in 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 that \(m = 2\) and \(b=-2\) (from the point \((0, -2)\)). So the equation of the line is \(y = 2x-2\).

Answer:

\(y = 2x - 2\)