Question

1. contest a radio station has $400 to give away for a contest. it gives away a $50 prize each week. the equation y = 400 - 50x represents the amount y the radio station has left to give away after x weeks. a. find the x - and y - intercepts and interpret their meaning in the context of the situation. b. graph the equation using the intercepts.

Explanation:

Step1: Find the y - intercept

Set \(x = 0\) in the equation \(y=400 - 50x\). Then \(y=400-50\times0=400\). In the context of the situation, the y - intercept of 400 means that at the start (week \(x = 0\)), the radio - station has $400 to give away for the contest.

Step2: Find the x - intercept

Set \(y = 0\) in the equation \(y = 400-50x\). Then \(0=400 - 50x\), which gives \(50x=400\), and \(x=\frac{400}{50}=8\). In the context of the situation, the x - intercept of 8 means that after 8 weeks, the radio - station will have given away all of the $400 (since the amount left to give away, \(y\), is 0).

To graph the equation, plot the y - intercept \((0,400)\) and the x - intercept \((8,0)\) and draw a straight line through them.

Answer:

The y - intercept is 400 (starting amount of money for the contest) and the x - intercept is 8 (number of weeks until all the money is given away).