Answer:
(a) The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.
Step-by-step explanation:
You want to find the y-intercept and slope from the given graph of candle height versus time.
Y-intercept
The y-intercept is the point on the y-axis where the graph intercepts the y-axis. This graph has a y-intercept of 9 inches, the height of the candle when it starts burning.
Slope
The slope of the graph is the ratio of "rise" to "run". Here, we can see that over a period of 3 hours, the candle loses 2 inches in height. That means the slope is ...
slope = rise/run = (-2 in)/(3 h) = -2/3 in/h
This slope means the candle height decreases 2/3 inch every hour.
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Additional comment
Your problem statement identifies points on the graph as (0, 9) and (3, 7). These are actually the points where we drew the "rise" and "run" lines in the attachment. They are points where the line crosses grid intersections, which are the best choice for finding slope.
The slope can be found algebraically as ...
m = (y2 -y1)/(x2 -x1) = (7 -9)/(3 -0) = -2/3
We find it is often easier to count grid squares.
