Acandle is 17 inches tall after burning for three hours. after five hours it is 15 inches 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 eight hours.

The time it burns is the independent variable. It is t.
The height is the dependent variable. It is h.

Use the information given to come up with two points.
Then you can find the equation.
Remember that we are using the time as t an the height as h.

17 inches and 3 hours is the ordered pair (3, 17).
15 inches and 5 hours is the ordered pair (5, 15).

We can now find the slope of the linear relation.

m = slope = (y2 - y1)/(x2 - x1) = (15 - 17)/(5 - 3) = -2/2 = -1

The slope is -1.

The point-slope form of the equation of a line is

y = mx + b

where m = slope, and b = y-intercept.

We know the slope, so we replace m with the slope, -1

y = mx + b

y = -1x + b

y = -x + b

We need to find b, the y-intercept.
We use one of our ordered pairs, and we substitute the x- and y-coordinates in for x and y in the equation and solve for b.

Let's use point (17, 3), so we have x = 17, and y = 3.

y = -x + b

3 = -17 + b

Add 17 to both sides

20 = b

b = 20

Now we rewrite the equation with our value of b, 20.

y = -x + b

y = -x + 20

Since we are asked to use t and h, we now have our equation:

h = -t + 20

After burning 8 hours, then t = 8

h = -t + 20

h = -8 + 20

h = 12

After burning 8 hours, the candle will be 12 inches tall.