We need to find the linear equation that describes the height of a candle that has been burning, in terms of the number of hours that it has been used.
We are given two points which we will use as points on the plane to represent the event, and which we are going to join with a line.
The first point is the pair: (1 , 7) which represents that after 1 hour of burning, the candle is 7 inches tall.
The second point is (2, 5) which represents that after 2 hours, the candle is 5 inches tall. Notice that we are using the time in hours in the frisr coordinate of the point. and the height of the candle in the second coordinate/position of the point. This is because we want our y axis to represent the height of the candle, and the x-axis to represent the time.
Now we proceed to find the slope that joins the two points (1, 7) and 2, 5), using the formula for slope:
slope = (7 - 5) / (1-2) = 2 / (-1) = -2
So the slope of the line is "-2".
Now we write the general form of a line in slope-intercept fashion:
y = m x + b
using m = -2 (our found slope)
y = -2 x + b
we use one of the points (for example (2, 5) to find the missing parameter "b":
5 = -2 (2) + b
5 = -4 + b
5 + 4 = b
b = 9
Therefore the function that reresents the height of the candle as it is being burned is:
y = -2 x + 9
where y is the candle's