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 \((-16, 0)\) and \((0, 8)\).

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-16,0)\) and \((x_2,y_2)=(0,8)\). Then \(m=\frac{8 - 0}{0 - (-16)}=\frac{8}{16}=\frac{1}{2}\).

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

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,8)\), we can see that \(b = 8\).

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 \(b = 8\) into the formula, we get \(y=\frac{1}{2}x+8\).

Answer:

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