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 -0.4 .
Suppose that the height of the candle after 13 hours is 24.8 centimeters. What was the height of the candle after 7 hours?
For items 7 and 8, refer to the situation below. The height (h) of the candle in centimeters is a function of time (t) in hours it has been burning.
Well, if the height of the candle is a linear function with a slope of -0.4, we can use the point-slope form of the equation to find the height after 7 hours.
The point-slope form is: y - y1 = m(x - x1)
Where:
y = height of the candle
m = slope of the line (-0.4)
x = time in hours
(x1, y1) = (13, 24.8)
So, let's plug in the values:
y - 24.8 = -0.4(x - 13)
Now, let's solve for y when x = 7:
y - 24.8 = -0.4(7 - 13)
y - 24.8 = -0.4(-6)
y - 24.8 = 2.4
y = 2.4 + 24.8
y = 27.2
Therefore, the height of the candle after 7 hours is approximately 27.2 centimeters. It's amazing how candles light up a room and melt at the same time. It's like a love-hate relationship with fire, don't you think?
To find the height of the candle after 7 hours, we can use the slope-intercept form of a linear function: y = mx + b, where y is the height of the candle, x is the amount of time it has been burning, m is the slope of the line, and b is the y-intercept.
Given that the slope of the line is -0.4, we can rewrite the equation as: y = -0.4x + b.
To find the value of b, we need to substitute the coordinates of a point on the line into the equation. We are given that the height after 13 hours is 24.8 centimeters, so we can substitute x = 13 and y = 24.8:
24.8 = -0.4(13) + b
Simplifying the equation:
24.8 = -5.2 + b
Adding 5.2 to both sides:
b = 24.8 + 5.2
b = 30
Now we can rewrite our equation: y = -0.4x + 30.
To find the height of the candle after 7 hours, we substitute x = 7 into the equation:
y = -0.4(7) + 30
Simplifying:
y = -2.8 + 30
y = 27.2
Therefore, the height of the candle after 7 hours is 27.2 centimeters.
To find the height of the candle after 7 hours, we can use the given information that the slope of the linear function is -0.4. We are also given that the height of the candle after 13 hours is 24.8 centimeters.
Let's use the equation of a linear function, which is represented as:
y = mx + b
Here, y represents the height of the candle, x represents the time in hours, m represents the slope, and b represents the y-intercept.
Using the information given, we can substitute the values into the equation:
24.8 = (-0.4) * 13 + b
Now, we can solve for b:
24.8 = -5.2 + b
Adding 5.2 to both sides:
24.8 + 5.2 = -5.2 + b + 5.2
30 = b
So, the y-intercept (b) is 30.
Now that we have the slope (m = -0.4) and the y-intercept (b = 30), we can substitute these values into the equation to find the height of the candle after 7 hours:
y = -0.4x + 30
Substituting x = 7:
y = -0.4 * 7 + 30
Calculating:
y = -2.8 + 30
y = 27.2
Therefore, the height of the candle after 7 hours is 27.2 centimeters.
h = -.4 t + b
24.8 = -.4(13) + b
b = 30
so
h = -.4 t + 30
h(7) = -.4(7)+30
= 27.2 cm