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 \((1, 0)\) (we can also choose 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 \((x_2,y_2)=(1,0)\). Then \(m=\frac{0 - (-2)}{1 - 0}=\frac{0 + 2}{1}=2\).

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 \(m = 2\) and from the point \((0,-2)\), the y - intercept \(b=-2\) (because when \(x = 0\), \(y=b\)). So substituting \(m = 2\) and \(b=-2\) into the equation, we get \(y=2x-2\).

Answer:

\(y = 2x-2\)