Question bank / Linear equations in two variables

Math · AlgebraMedium

Marisol earns $25\$25 per hour tutoring and $40\$40 per hour designing websites. The equation 25x+40y=1,00025x + 40y = 1{,}000 represents the numbers of hours she can spend tutoring, xx, and designing websites, yy, to earn exactly $1,000\$1{,}000. The graph of the equation in the xyxy-plane has a yy-intercept of (0,25)(0, 25). What is the best interpretation of this intercept?

A

If Marisol does no tutoring, she must design websites for 2525 hours to earn $1,000\$1{,}000.

B

If Marisol designs no websites, she must tutor for 2525 hours to earn $1,000\$1{,}000.

C

Marisol earns $25\$25 for each hour she spends designing websites.

D

Marisol works a total of 2525 hours to earn $1,000\$1{,}000.

Show answer and explanation

Answer: A

At the yy-intercept, x=0x = 0, so Marisol does no tutoring. The equation becomes 40y=1,00040y = 1{,}000, so y=25y = 25. The intercept (0,25)(0, 25) means she must design websites for 2525 hours if she does no tutoring.

Choice B mixes up the variables. At the yy-intercept, the tutoring hours, xx, equal 00.

Why the other choices are wrong

  • B. At the y-intercept, x is 0, so she does no tutoring. Tutoring alone would take 1,000 ÷ 25 = 40 hours.
  • C. She earns $40 per hour designing websites. The 25 in the intercept is a number of hours.
  • D. Her total hours depend on how she splits her time. 25 hours is her design time only when she does no tutoring.
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