what is the height of the candle after 14 hours

Question

The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives a line with a slope of -0.5

Suppose that the height of the candle after 17 hours is 21.5cm what was the height of the candle after 14 hours?

Answer 1

"The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning" means the x-axis is time (hrs) and the y-axis is height (cm).

Use the point-slope form of a line:

y - y₁ = m(x - x₁)

where "m" is the slope and (x₁, y₁) is a point on the line.

You have been give the slope so m = -0.5 and you have been given a point "after 17 hours is 21.5cm" so x₁ = 17 and y₁ = 21.5 so:

y - y₁ = m(x - x₁)

y - 21.5 = -0.5(x - 17)

y - 21.5 = -0.5x + 8.5

y = -0.5x + 30 or, using "h" for height and "t" for time:

h(t) = -0.5t + 30

h(14) = -0.5(14) + 30 = -7 + 30 = 23 cm