Question

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

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((0, -6)\) (the y - intercept) and \((3, -7)\) (we can also choose other points, but these are easy to identify).

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

The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Let \((x_1,y_1)=(0, - 6)\) and \((x_2,y_2)=(3, - 7)\).
Then \(m=\frac{-7-(-6)}{3 - 0}=\frac{-7 + 6}{3}=\frac{-1}{3}=-\frac{1}{3}\).

Step3: Use the 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 the y - intercept \(b=-6\) (since the line crosses the y - axis at \((0,-6)\)) and \(m =-\frac{1}{3}\).
Substituting these values into the slope - intercept form, we get \(y=-\frac{1}{3}x-6\).

Answer:

\(y = -\frac{1}{3}x - 6\)