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A party planner organized a dinner party. The party planner recorded the height of the candlesticks over time and graphed the relationship.

graph with the x axis labeled time in hours and the y axis labeled height of candlestick in inches and a line going from the point 0 comma 8 through the point 3 comma 6

Find and interpret the slope and y-intercept in this real-world situation.
The slope is 8, and the y-intercept is negative two thirds. The candle starts at a height of two thirds of an inch and decreases 8 inches every hour.
The slope is 8, and the y-intercept is negative three halves. The candle starts at a height of three halves of an inch and decreases 8 inches every hour.
The slope is negative two thirds, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases two thirds of an inch every hour.
The slope is negative three halves, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases three halves of an inch every hour.

1 answer

To find the slope and y-intercept from the points given on the graph, we will analyze the points (0, 8) and (3, 6).

  1. Determine the slope (m):

The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (0, 8) as \((x_1, y_1)\) and (3, 6) as \((x_2, y_2)\):

\[ m = \frac{6 - 8}{3 - 0} = \frac{-2}{3} \]

The slope is -2/3, indicating that for every hour that passes, the height of the candlestick decreases by 2/3 of an inch.

  1. Determine the y-intercept (b):

The y-intercept is the value of y when x = 0. Based on the graph, when time is 0 hours, the height of the candlestick is 8 inches. Therefore:

\[ b = 8 \]

  1. Conclusion:

So the slope is -2/3, and the y-intercept is 8. This means that the candlestick starts at a height of 8 inches and decreases by 2/3 of an inch every hour.

Interpretation: The correct response is: "The slope is negative two thirds, and the y-intercept is 8. The candle starts at a height of 8 inches and decreases two thirds of an inch every hour."