Question

A candle is 18 in. tall after burning for 3 hours. After 5 hours, it is 16.5 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.

a. h(t) = -0.75t + 20.25; 14.25 inches
b. h(t) = 0.75t + 15.75; 9.75 inches
c. h(t) = -0.75t + 15.75; 9.75 inches
d. h(t) = 0.75t + 20.25; 14.25 inches

Answer 1

To write a linear equation to model the relationship between the height of the candle and time, we can use the information given. We know that after 3 hours, the candle is 18 inches tall, and after 5 hours, it is 16.5 inches tall.

We can set up a system of linear equations to represent this information. Let's call the height of the candle h and the time t. Then we can set up the following system:

h = 18 - 3t

h = 16.5 - 5t

To solve this system, we can set the two equations equal to each other and solve for t:

18 - 3t = 16.5 - 5t

1.5 = 2t

t = 0.75

This tells us that the height of the candle decreases by 0.75 inches per hour.

Now we can use this information to predict how tall the candle will be after 8 hours. We can plug in 8 for t in the equation h = 18 - 3t to find the height of the candle:

h = 18 - 3(8)

h = 18 - 24

h = -6 inches

So the candle will be about 6 inches shorter after burning for 8 hours. This means it will be about 10.5 inches tall.

The correct option is c, h(t) = -0.75t + 15.75; 9.75 inches.

This is because we found that the height of the candle decreases by 0.75 inches per hour, which is represented by the coefficient of t in the equation. The y-intercept, 15.75, represents the initial height of the candle, which we found to be 16.5 inches.

Happy to help!

Answer 2

Answer: To write a linear equation to model the relationship between the height h of the candle and time t, we need to find the slope and y-intercept of the line that represents this relationship.

The slope of the line is given by the rise over the run, or the change in the y-value (the height of the candle) over the change in the x-value (the time). We can calculate the slope by taking the difference in the height of the candle after 5 hours and 3 hours, and dividing it by the difference in the time:

slope = (16.5 - 18) / (5 - 3) = (-1.5) / (2) = -0.75

The y-intercept of the line is the point at which the line crosses the y-axis. This is the height of the candle when the time is 0. We can use the height of the candle after 3 hours as the y-intercept, since this is the height when the time is 3:

y-intercept = 18

We can use these values to write a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.

Plugging in the values we found, we get:

h(t) = -0.75t + 18

This is the linear equation that models the relationship between the height h of the candle and time t.

To predict how tall the candle will be after burning for 8 hours, we can plug in t = 8 into the equation:

h(8) = -0.75(8) + 18 = -6 + 18 = 12 inches

This means that the candle will be 12 inches tall after burning for 8 hours.

Therefore, the correct answer is (d) h(t) = 0.75t + 20.25; 14.25 inches.