a candle is 15 inches tall after buring r 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 buring 8 hours
Let h represent the height of the candle (in inches) and r represent the number of hours the candle has been burning.
Given that the candle is 15 inches tall after burning r hours, we can write the equation:
h = 15 - r
After 5 hours, the candle is 13 inches tall. Plugging in r = 5 into the equation, we get:
13 = 15 - 5
Simplifying the equation gives:
13 = 10
This is not true and indicates an error in the problem statement. After 5 hours, the candle cannot be 13 inches tall if it starts at 15 inches. Please double-check the information provided.
We cannot predict how tall the candle will be after burning 8 hours without accurate data.
To write a linear equation that models the relationship between the height of the candle and the number of hours it has burned, we can use the slope-intercept form of a linear equation, y = mx + b.
Given:
Initial height of the candle, y = 15 inches
Height of the candle after 5 hours, y = 13 inches
To find the slope (m):
Change in height = 13 - 15 = -2 inches
Change in time = 5 - 0 = 5 hours
Slope (m) = change in height / change in time = -2 / 5
Using the slope-intercept form:
y = mx + b
Substituting the known values:
13 = (-2/5) * 5 + b
Simplifying:
13 = -2 + b
b = 15
Therefore, the linear equation that models the relationship between the height of the candle and the number of hours it has burned is:
y = (-2/5) * x + 15
To predict how tall the candle will be after burning 8 hours, substitute x = 8 into the equation:
y = (-2/5) * 8 + 15
y = (-16/5) + 15
y = -16/5 + 75/5
y = 59/5
After burning 8 hours, the candle is predicted to be approximately 11.8 inches tall.
To write a linear equation to model the relationship between the height of the candle and the number of hours it has burned, we need to find the slope and y-intercept of the equation.
Given that the candle is 15 inches tall after burning r hours and it is 13 inches tall after 5 hours, we can use this information to find the slope.
The change in height is 15 - 13 = 2 inches.
The change in hours is r - 5.
Thus, the slope of the linear equation is:
slope = change in height / change in hours = 2 / (r - 5)
Now, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
Using the point (5, 13), our equation becomes:
y - 13 = (2 / (r - 5))(x - 5)
Simplifying, we can write the linear equation as:
y = (2 / (r - 5))(x - 5) + 13
To predict how tall the candle will be after burning 8 hours, substitute x = 8 into the equation:
y = (2 / (r - 5))(8 - 5) + 13
Simplifying further will give you the predicted height of the candle after burning 8 hours.