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A candle is 17 in. tall after burning for 3 hours. After 5 hours, it is 15 in. tall. Write a linear equation to model the relationship between height h of the candle and time t. Predict how tall the candle will be after burning 8 hours.
To write a linear equation to model the relationship between height h of the candle and time t, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope of the line. The slope is the change in height divided by the change in time.
Change in height = 15 in. - 17 in. = -2 in.
Change in time = 5 hours - 3 hours = 2 hours
Slope (m) = change in height / change in time
= -2 in. / 2 hours
= -1 in./hour
Next, we can use one of the given points (3 hours, 17 in.) to find the y-intercept (b).
Using the point-slope form of a linear equation, we have:
h - 17 = -1(t - 3)
h - 17 = -t + 3
h = -t + 3 + 17
h = -t + 20
So, the linear equation that models the relationship between height h and time t for the candle is:
h = -t + 20
To predict how tall the candle will be after burning for 8 hours, we can substitute t = 8 into the equation and solve for h:
h = -(8) + 20
h = -8 + 20
h = 12
Therefore, the candle will be 12 inches tall after burning for 8 hours.