Question

this question has two parts. first, answer part a. then, answer part b.
part a
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.
the x - intercept is
this means that after
weeks, the radio station will have $
left to give away. the y - intercept is
this means that the radio station initially had $
to give away.
part b
b. graph the equation using the intercepts.
a)
500
450
400
350
300
250
200
150
100
50
amount to give away

Explanation:

Part A

Step 1: Find x - intercept

To find the x - intercept, we set \(y = 0\) in the equation \(y=400 - 50x\).

$$
LATEXBLOCK0
$$

The x - intercept is 8. In the context of the problem, this means that after 8 weeks, the radio station will have $0 left to give away (since \(y = 0\) at \(x = 8\)).

Step 2: Find y - intercept

To find the y - intercept, we set \(x = 0\) in the equation \(y = 400-50x\).

$$ y=400-50\times0=400 $$

The y - intercept is 400. This means that the radio station initially (when \(x = 0\), i.e., at week 0) had $400 to give away.

To graph the equation \(y = 400-50x\) using the intercepts:

1. We know the x - intercept is at the point \((8,0)\) (since when \(y = 0\), \(x = 8\)) and the y - intercept is at the point \((0,400)\) (since when \(x = 0\), \(y = 400\)).
2. Plot the point \((0,400)\) on the y - axis (where the amount to give away is on the y - axis and the number of weeks is on the x - axis) and the point \((8,0)\) on the x - axis.
3. Then draw a straight line connecting these two points. Looking at the given option A, the line passes through \((0,400)\) and \((8,0)\) which matches our intercepts.

Answer:

The x - intercept is \(\boldsymbol{8}\). This means that after \(\boldsymbol{8}\) weeks, the radio station will have \(\boldsymbol{0}\) left to give away. The y - intercept is \(\boldsymbol{400}\). This means that the radio station initially had \(\boldsymbol{400}\) to give away.

Part B