Question

write the equation of the line in fully simplified slope-intercept form.
answer attempt 1 out of 2
answer:

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, -8)\) (the y - intercept) and another point, for example, \((2, -9)\).

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 8)\) and \((x_2,y_2)=(2, - 9)\). Then \(m=\frac{-9-(-8)}{2 - 0}=\frac{-9 + 8}{2}=\frac{-1}{2}=-\frac{1}{2}\).

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 \(m =-\frac{1}{2}\) and \(b=-8\) (from the point \((0,-8)\)). So the equation of the line is \(y =-\frac{1}{2}x-8\).

Answer:

\(y =-\frac{1}{2}x - 8\)