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

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

The formula for the 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 \((0, 4)\) as \((x_1,y_1)\) and \((2, 0)\) as \((x_2,y_2)\), we have:
\(m=\frac{0 - 4}{2-0}=\frac{- 4}{2}=-2\)

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 \(m=-2\) and from the point \((0, 4)\), the y - intercept \(b = 4\).
Substituting these values into the slope - intercept form, we get \(y=-2x + 4\)

Answer:

\(y=-2x + 4\)