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 \((0, 5)\) (the y - intercept) and \((2, - 7)\).

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 \((x_2,y_2)=(2,-7)\). Then \(m=\frac{-7 - 5}{2 - 0}=\frac{-12}{2}=- 6\).

Step3: Write the equation in slope - intercept form

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 \(m=-6\) and \(b = 5\) (from the point \((0,5)\)). So the equation is \(y=-6x + 5\).

Answer:

\(y=-6x + 5\)