Question

what equations does the graph show?
write the equations in slope - intercept form. simplify any fractions.
y =
y =

Explanation:

Step1: Analyze the blue line

The blue line intersects the y - axis at (0, 6), so the y - intercept \(b = 6\). We can find another point on the blue line, for example, when \(x = 3\), \(y=0\) (from the graph). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 6}{3 - 0}=\frac{- 6}{3}=-2\). Using the slope - intercept form \(y=mx + b\), the equation of the blue line is \(y=-2x + 6\).

Step2: Analyze the green line

The green line intersects the y - axis at (0, 3), so the y - intercept \(b = 3\). We can find another point on the green line, for example, when \(x = 6\), \(y = 0\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 3}{6 - 0}=\frac{-3}{6}=-\frac{1}{3}\). Using the slope - intercept form \(y = mx + b\), the equation of the green line is \(y=-\frac{1}{3}x+3\).

Answer:

\(y=-2x + 6\)
\(y =-\frac{1}{3}x + 3\)