Question

write the equation of this line in slope-intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((-12, 0)\) and \((0, -6)\).

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-12,0)\) and \((x_2,y_2)=(0, -6)\). Then \(m=\frac{-6 - 0}{0 - (-12)}=\frac{-6}{12}=-\frac{1}{2}\).

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

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,-6)\), we can see that \(b=-6\).

Step4: Write the equation in slope - intercept form

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m =-\frac{1}{2}\) and \(b=-6\) into the formula, we get \(y=-\frac{1}{2}x-6\).

Answer:

\(y = -\frac{1}{2}x - 6\)