Acandle is 17in tall after burning for 3 hours, after 5 hours , it is 15in tall. write a linear equation to model the relationship between height h of the candle and time t. predict how tall the candle will be after burning 8 hours

 You have a candle that is decreasing its height over a period of time. You want to know at what rate it is changing. Since the height is measured in inches and the time is measured in hours, the decreasing rate will have units of inches per hour, which means it will be a fraction. The numerator will include the change in height and the denominator will be the change in time. 

change in height . . 17 inches - 15 inches . . . 2 inches . . . . inch 
= = = 1  
change in time . . . . . 5 hours - 3 hours. . . . . 2 hours . . . . . hour 

We have a rate constant of 1 inch per hour. 
We also have variable h with units of inches, and we also have variable t with units in hours. 
So we begin the equation with the two variables like this 
h (in inches) = t (in hours) 
We know that this is an incomplete equation because the constant rate is not included. 
Since the constant rate has units of inches per hour, if we multiply the right side by the constant, the equation becomes 
h (inches) = t (hours) * rate (inches/hour) 
notice how the hour units cancel out on the right side, leaving us with just inches? 
Therefore, that is the correct form for this equation. 
However, this equation only calculates how much the candle will decrease in height over time. 
To calculate the new height after a decrease, we need to include a reference height and time. 
In this case, since we are not given the original height before any burning, then we have to use either the 17 inch height after 3 hours, or the 15 inch height after 5 hours. 
The equation becomes 
h = reference height - (t - reference time)(rate) 
If we use the reference height of 17 inches, then the reference time is 3 hours 
If we use the reference height of 15 inches, then the reference time is 5 hours. 

Using this equation with the reference height of 15 inches and reference time of 5 hours, after 8 hours, the candle's new height becomes 
h = reference height - (t - reference time)(rate) 
h = 15 - (8 - 5)(1) 
h = 15 - 3 
h = 12 inches tall after 8 hours