Question

movie ticket sales : $6x + 9y = 1,500$
which graph shows this relationship?
three graphs with red lines and grid, each with x-axis (0,100,200) and y-axis (0,20,60,100,140) are shown as options, along with radio buttons and a done button

Explanation:

Step1: Find x-intercept (y=0)

Set \( y = 0 \) in \( 6x + 9y = 1500 \):
\( 6x + 9(0) = 1500 \)
\( 6x = 1500 \)
\( x = \frac{1500}{6} = 250 \)

Step2: Find y-intercept (x=0)

Set \( x = 0 \) in \( 6x + 9y = 1500 \):
\( 6(0) + 9y = 1500 \)
\( 9y = 1500 \)
\( y = \frac{1500}{9} \approx 166.67 \)

Step3: Analyze graphs

The line should cross the x - axis at \( x = 250 \) and y - axis near \( y \approx 166.67 \). The second graph (middle one) has an x - intercept around 250 and y - intercept around 166 (close to our calculation), matching the intercepts.

Answer:

The middle graph (the second option among the three) shows the relationship \( 6x + 9y = 1500 \).