a candle is 15 inches tall after burning 3 hours after 5 hours it is 13 inches tall
write a linear equation to model the relationship between height of the calndle and predict how tall the candle will be after burning 8 hours
To write a linear equation to model the relationship between the height of the candle and the time it has been burning, we can use the equation of a line: y = mx + b, where y represents the height of the candle and x represents the time in hours.
Let's first find the slope (m) of the line using the given information:
The initial height of the candle (when x = 0) is 15 inches, and after 3 hours (when x = 3), the height is 15 - 3 = 12 inches.
Therefore, we can calculate the slope (m) as:
m = (change in y) / (change in x) = (12 - 15) / (3 - 0) = (-3) / (3) = -1.
Now let's find the y-intercept (b) using the initial height information:
When x = 0, y = 15. Thus, b = 15.
Now we can write the linear equation:
y = mx + b
Height = -1 * (time) + 15
Height = -1x + 15
To predict how tall the candle will be after burning 8 hours, we substitute x = 8 into the equation:
Height = -1(8) + 15
Height = -8 + 15
Height = 7 inches.
Therefore, the candle is predicted to be 7 inches tall after burning for 8 hours.
To write a linear equation that models the relationship between the height of the candle and the burning time, we can use the two given data points: (3, 15) and (5, 13).
First, we need to determine the slope of the line. The slope (m) represents the change in height divided by the change in time.
m = (change in height) / (change in time)
= (13 - 15) / (5 - 3)
= -2 / 2
= -1
Next, we can use the point-slope form of a linear equation to write the equation:
y - y1 = m(x - x1)
Using one of the given points (3, 15):
y - 15 = -1(x - 3)
y - 15 = -x + 3
y = -x + 3 + 15
y = -x + 18
Now, to predict the height of the candle after burning for 8 hours, we substitute x = 8 into the equation:
y = -8 + 18
y = 10
Therefore, the predicted height of the candle after burning for 8 hours is 10 inches.
To model the relationship between the height of the candle and the burning time, we can use a linear equation. Let's use the slope-intercept form of a linear equation, which is y = mx + b, where y represents the height of the candle and x represents the burning time.
First, we need to find the slope (m). The slope represents the change in height (y) with respect to the change in time (x). We can calculate the slope using the formula: m = (y2 - y1) / (x2 - x1).
Using the given information, let's calculate the slope:
y1 = 15 inches (height after 3 hours)
y2 = 13 inches (height after 5 hours)
x1 = 3 hours
x2 = 5 hours
m = (13 - 15) / (5 - 3)
m = -2 / 2
m = -1
Now that we have the slope, we can find the y-intercept (b) using the formula: b = y - mx. We can choose any point (x, y) on the line to calculate the y-intercept.
Let's use the point (5, 13):
b = 13 - (-1)(5)
b = 13 + 5
b = 18
Now we have the slope (m = -1) and the y-intercept (b = 18). We can write the linear equation representing the relationship between the height of the candle (y) and the burning time (x):
y = -1x + 18
To predict the height of the candle after burning 8 hours, we substitute x = 8 into the equation:
y = -1(8) + 18
y = -8 + 18
y = 10
Therefore, the predicted height of the candle after burning 8 hours is 10 inches.