Question

write the equation of the line in fully simplified slope - intercept form.

Explanation:

Step1: Find two points on the line

From the graph, two points are \((0, - 6)\) and \((4,-5)\).

Step2: Calculate the slope \(m\)

Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,-6)\) and \((x_2,y_2)=(4,-5)\). Then \(m=\frac{-5-(-6)}{4 - 0}=\frac{-5 + 6}{4}=\frac{1}{4}\).

Step3: Use the slope - intercept form \(y=mx + b\)

We know that \(m=\frac{1}{4}\) and from the point \((0,-6)\), when \(x = 0\), \(y=-6\), so \(b=-6\).

Answer:

\(y=\frac{1}{4}x-6\)