Question

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

Explanation:

Step1: Analyze the purple line

The purple line has a y - intercept of \( b = 2 \) (it crosses the y - axis at \( (0,2) \)) and an x - intercept of \( (6,0) \). The slope \( m \) is calculated as \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 2}{6 - 0}=\frac{-2}{6}=-\frac{1}{3} \). Using the slope - intercept form \( y=mx + b \), the equation of the purple line is \( y =-\frac{1}{3}x+2 \).

Step2: Analyze the blue line

The blue line has a y - intercept of \( b=-6 \) (it crosses the y - axis at \( (0, - 6) \)) and an x - intercept of \( (-2,0) \). The slope \( m \) is calculated as \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0-(-6)}{-2 - 0}=\frac{6}{-2}=-3 \). Using the slope - intercept form \( y = mx + b \), the equation of the blue line is \( y=-3x - 6 \).

Answer:

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