Question

write an equation of the line below.

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 \((3, 4)\).

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((0, -2)\) and \((3, 4)\), we have \(x_1 = 0,y_1=-2,x_2 = 3,y_2 = 4\). Then \(m=\frac{4-(-2)}{3 - 0}=\frac{6}{3}=2\).

Step3: Write the equation in slope - intercept form (\(y=mx + b\))

We know that \(m = 2\) (the slope) and \(b=-2\) (the y - intercept, since the line crosses the y - axis at \((0,-2)\)). So the equation of the line is \(y=2x-2\).

Answer:

\(y = 2x-2\)