Question 2
Answer: 1.20
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To get this answer, you divide the total amount of royalties (300) over the number of books (250) to get 300/250 = 1.20
Another way to see this is through the ratio of
300 dollars: 250 books
then you divide both parts of that ratio by 250 so that the "250 books" turns into "1 book" like so...
300 dollars: 250 books
300/250 dollars: 250/250 books
1.20 dollars: 1 book
Indicating that his royalties per book is 1.20 dollars. The rate of change is often expressed as a unit rate, meaning that we want the royalties for 1 book (which then scales up).
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Question 3
Answer: slope is -1/10 or -0.1; slope tells us how much the candle height is decreasing each minute, y intercept is the starting candle height (see below for further explanation)
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Explanation:
The y intercept is at 25, as this is where the diagonal line crosses the vertical y axis. Similarly, the x intercept is 250. The y and x intercept lead to the two points (0,25) and (250,0). Let's use the slope formula to find the slope of the line through these two points
m = (y2 - y1)/(x2 - x1)
m = (0 - 25)/(250 - 0)
m = -25/250
m = -1/10
m = -0.1
The slope of the line is -1/10 or the decimal equivalent -0.1
What does the slope tell us? It tells us how much of the candle's height is changing as each minute ticks by. Specifically, the slope -0.1 means that the candle height is going down by 0.1 cm for each minute gone by. A shorter way to say this is to say "the height is decreasing by 0.1 cm per minute" (think of it like a speed such as miles per hour)
The y intercept is the starting height of the candle due to the fact that x = 0 here. Therefore, the starting height of the candle is 25 cm.
Side note: the x intercept of 250 tells us how long the candle burns for, which in this case is 250 minutes (4 hrs, 10 min) because y = 0 for the x intercept, and y is the height of the candle at time x. Anything beyond x = 250 is not possible in realistic sense as we can't have a negative y height value.
