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 −0.6
Suppose that the height of the candle after 19 hours is
9.6 centimeters. What was the height of the candle after 13 hours?
13 hours is 6 hrs less than 19 hours.
So, add 6(0.6) to the height.
The slope of the graph is –1. Which statement describes how the slope is related to the burning of a candle?
To find the height of the candle after 13 hours, we can use the given information that the slope of the line representing the height-time function is -0.6.
Let's denote the height of the candle after 13 hours as H.
We can use the point-slope form of a linear equation to represent the height-time function:
H - H1 = m(T - T1)
where H1 and T1 are the height and time values of a point on the line, respectively, and m is the slope of the line.
Substituting the given information into the equation, we have:
H - 9.6 = -0.6(13 - 19)
Now, we can simplify and solve for H:
H - 9.6 = -0.6(-6)
H - 9.6 = 3.6
Adding 9.6 to both sides of the equation, we get:
H = 3.6 + 9.6
H = 13.2
Therefore, the height of the candle after 13 hours is 13.2 centimeters.
To find the height of the candle after 13 hours, we can use the given information about the slope of the linear function and the height of the candle after 19 hours.
We know that the height of the candle is a linear function of time with a slope of -0.6. This means that for every hour the candle burns, its height decreases by 0.6 centimeters.
So, to find the height of the candle after 13 hours, we can subtract the amount the height decreases over 13 hours from the height after 19 hours.
First, let's calculate the amount the height decreases over 13 hours:
Height decrease over 13 hours = slope * time
Height decrease over 13 hours = -0.6 * 13
Height decrease over 13 hours = -7.8 centimeters
Next, let's subtract the height decrease over 13 hours from the height after 19 hours:
Height after 13 hours = Height after 19 hours - Height decrease over 13 hours
Height after 13 hours = 9.6 - 7.8
Height after 13 hours = 1.8 centimeters
Therefore, the height of the candle after 13 hours is 1.8 centimeters.