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.
12 inches tall
To write a linear equation to model the relationship between the height h of the candle and time t, we can use the slope-intercept form of a linear equation, which is y = mx + b.
Let's assign h as the dependent variable (y) and t as the independent variable (x).
We know that after 3 hours, the height of the candle is 17 inches, and after 5 hours, the height is 15 inches.
So, we can use these two points to find the slope (m) and the y-intercept (b).
The slope can be calculated as (change in y) / (change in x):
m = (15 - 17) / (5 - 3) = -2 / 2 = -1
Now, let's substitute one of the two points into the equation to find the y-intercept (b). We'll use the point (3, 17):
17 = -1 * 3 + b
17 = -3 + b
b = 17 + 3
b = 20
Now we have the slope (m = -1) and the y-intercept (b = 20), so we can write the linear equation:
h = -t + 20
To predict how tall the candle will be after burning for 8 hours, we substitute t = 8 into the equation:
h = -(8) + 20
h = -8 + 20
h = 12
Therefore, the candle will be 12 inches tall after burning for 8 hours.
To write a linear equation to model the relationship between the height h of the candle and time t, we can use the slope-intercept form of a linear equation: y = mx + b.
Let's begin by finding the slope (m) of the line. The slope represents the rate of change, which in this case is the change in height of the candle per hour. We can calculate the slope by using the formula:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are two points on the line.
Given that after 3 hours the candle is 17 inches tall and after 5 hours it is 15 inches tall, we can set our points as (3, 17) and (5, 15):
m = (15 - 17) / (5 - 3)
m = -2 / 2
m = -1
Now that we have the slope, we can use one of the points (3, 17) to find the y-intercept (b). Plugging the values into the equation y = mx + b:
17 = (-1)(3) + b
17 = -3 + b
b = 17 + 3
b = 20
So, the equation to model the relationship between the height (h) of the candle and time (t) is:
h = -t + 20
To predict how tall the candle will be after burning for 8 hours, we need to substitute t = 8 into the equation:
h = -(8) + 20
h = -8 + 20
h = 12
Therefore, the candle is predicted to be 12 inches tall after burning for 8 hours.
since it burned 2 inches in 2 hours,
it burned 1 inch per hour.
SO, it must have burned 3 inches in the first 3 hours
h(t) = 20 - t