Question

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

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((0, -8)\) (the y - intercept) and \((2, 0)\) (where the line crosses the x - axis).

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

The formula for the slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Using the points \((0,-8)\) as \((x_1,y_1)\) and \((2,0)\) as \((x_2,y_2)\), we have:
\(m=\frac{0 - (-8)}{2 - 0}=\frac{0 + 8}{2}=\frac{8}{2}=4\)

Step3: Write the equation in slope - intercept form

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 \(m = 4\) and from the point \((0,-8)\), the y - intercept \(b=-8\).
Substituting these values into the slope - intercept form, we get \(y = 4x-8\)

Answer:

\(y = 4x-8\)