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 the points \((4, 0)\) and \((8, 6)\) (we can also use other clear points, but these are easy to identify).

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

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(4,0)\) and \((x_2,y_2)=(8,6)\). Then \(m = \frac{6 - 0}{8 - 4}=\frac{6}{4}=\frac{3}{2}\).

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

We use the slope - intercept form \(y=mx + b\) and one of the points. Let's use the point \((4,0)\) and \(m=\frac{3}{2}\). Substitute into \(y=mx + b\):
\(0=\frac{3}{2}(4)+b\)
\(0 = 6 + b\)
Subtract 6 from both sides: \(b=- 6\).

Step4: Write the equation in slope - intercept form

The slope - intercept form is \(y=mx + b\). We know that \(m = \frac{3}{2}\) and \(b=-6\), so the equation is \(y=\frac{3}{2}x-6\).

Answer:

\(y=\frac{3}{2}x - 6\)