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. What is the height of the candle after it has been burning for 8 hrs?
The candle has burned up (8hrs)(0.4cm/hr).
To find the height of the candle after it has been burning for 8 hours, we can use the equation of a linear function, which is in the form y = mx + b, where y is the dependent variable (in this case, the height of the candle), x is the independent variable (in this case, the time in hours), m is the slope, and b is the y-intercept.
Given that the slope of the line representing the height of the candle is 0.4, we have m = 0.4. However, since we don't have the y-intercept (b), we cannot directly use the equation y = mx + b to find the height.
To proceed, we need at least one point through which the line passes so that we can find the y-intercept. Let's assume that when the candle starts burning (at 0 hours), its height is h0 centimeters.
Now, using the slope-intercept form of the equation, we have the equation of the line representing the height of the candle: y = 0.4x + h0.
Since we know that the candle starts burning at 0 hours and its height at that time is h0, we plug in x = 0 and solve for h0:
h0 = 0.4(0) + h0
h0 = 0 + h0
h0 = h0
The equation shows that the height of the candle when it starts burning is equal to the height of the candle when it starts burning, which makes sense.
Now, we can use the equation y = 0.4x + h0 to find the height of the candle after 8 hours. Plugging in x = 8, we get:
y = 0.4(8) + h0
y = 3.2 + h0
Since we do not have the value of h0, we cannot find the exact height of the candle after 8 hours without further information. But we can determine the height relative to its initial height.