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 \((0, -2)\) (the y - intercept) and \((1, -9)\) (we can also use other points, but these are easy to identify).

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 2)\) and \((x_2,y_2)=(1, - 9)\). Then \(m=\frac{-9-(-2)}{1 - 0}=\frac{-9 + 2}{1}=\frac{-7}{1}=-7\).

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 \(m=-7\) and from the point \((0, - 2)\), the y - intercept \(b=-2\). So the equation of the line is \(y=-7x-2\).

Answer:

\(y = - 7x-2\)