Question

q. write the equation of the line in slope - intercept form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((0, -4)\) (the y - intercept) and \((2, 0)\).

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

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

Step3: Determine the y - intercept (\(b\))

The slope - intercept form of a line is \(y=mx + b\), where \(b\) is the y - intercept.
We know that the line crosses the y - axis at \((0,-4)\), so \(b=-4\).

Step4: Write the equation in slope - intercept form

Substitute \(m = 2\) and \(b=-4\) into the slope - intercept form \(y=mx + b\).
We get \(y = 2x-4\)

Answer:

\(y = 2x-4\)