Let's assume that the linear equation to model the relationship between the height of the fire, h, and the time, t, is of the form h = mt + b, where m is the slope of the line and b is the y-intercept.
To find the slope, we can use the formula m = (y2 - y1) / (x2 - x1) with the points (4, 24) and (6, 20).
m = (20 - 24) / (6 - 4)
m = -4 / 2
m = -2
Using the point-slope form of a linear equation, we can now substitute one of the points, (4, 24), into the equation to find b:
24 = -2(4) + b
24 = -8 + b
b = 24 + 8
b = 32
Therefore, the linear equation that models the relationship between the height of the fire, h, and the time, t, is h = -2t + 32.
To predict how tall the fire will be after burning 8 hours, we substitute t = 8 into the equation:
h = -2(8) + 32
h = -16 + 32
h = 16
Therefore, the fire will be 16 inches tall after burning for 8 hours.
A campfire has a flame 24 inches tall after burning for 4 hours. After 6 hours, it is 20 inches tall.
Write a linear equation to model the relationship between height h of the fire and time t. Predict how tall the fire will be after burning 8 hours.
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