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 \((-6, 7)\) and \((0, -8)\) (the y - intercept is at \((0, -8)\)).

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

The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-6,7)\) and \((x_2,y_2)=(0, - 8)\). Then \(m=\frac{-8 - 7}{0-(-6)}=\frac{-15}{6}=-\frac{5}{2}\).

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 \(m =-\frac{5}{2}\) and from the point \((0,-8)\), \(b=-8\). So the equation of the line is \(y=-\frac{5}{2}x - 8\).

Answer:

\(y = -\frac{5}{2}x-8\)