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 \((0, -2)\) (the y - intercept) and \((2, 4)\).

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 \((x_2,y_2)=(2,4)\). Then \(m=\frac{4-(-2)}{2 - 0}=\frac{4 + 2}{2}=\frac{6}{2}=3\).

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 \(m = 3\) and from the point \((0,-2)\), \(b=-2\). So the equation of the line is \(y = 3x-2\).

Answer:

\(y = 3x-2\)