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

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((0, -1)\) and \((2, -5)\), we have \(x_1 = 0,y_1=-1,x_2 = 2,y_2=-5\).
So \(m=\frac{-5-(-1)}{2 - 0}=\frac{-5 + 1}{2}=\frac{-4}{2}=-2\).

Step3: Write the equation in 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 \(m=-2\) and from the point \((0,-1)\), the y - intercept \(b=-1\).
Substituting \(m=-2\) and \(b = - 1\) into the slope - intercept form, we get \(y=-2x-1\).

Answer:

\(y = - 2x-1\)