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 \((0, 5)\) (the y - intercept) and \((1, - 2)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,5)\) and \((x_2,y_2)=(1, - 2)\). Then \(m=\frac{-2 - 5}{1-0}=\frac{-7}{1}=-7\).

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

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 \(m=-7\) and from the point \((0,5)\), the y - intercept \(b = 5\). So substituting \(m=-7\) and \(b = 5\) into the slope - intercept form, we get \(y=-7x + 5\).

Answer:

\(y=-7x + 5\)