Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. after 9 hours of burning, a candle has a height of 17.5 centimeters. after 24 hours of burning, its height is 22 centimeters. what is the height of the candle after 22 hours?

 The candle has a height of 21.4 cm after burning for 22 hours.

Step-by-step explanation:

let x=hours, m=rate of change,  and  y= candle height

First you have to find the slope or, rate of change using the slope formula.  y2-y1 divided by x2-x1   .        

Here is our points    (9,     17.5)   and   (24,    22)

                                    x1       y1                 x2     y2

Now we put these into the equation and solve

  =

Now that we have the slope of 3/10 we can use this to find the y-intercept using the point-slope equation.

                y-17.5= .3(x-9) Solve

y-17.5=.3x-2.7                                        y  -14.8=      .3x

 +2.7         +2.7                                         +14.8               +14.8

y=.3x+14.8                     the y-intercept is 14.8

Now we use this equation to  plug in the 22 hours.

y=.3(22) +14.8

y=6.6+14.8

y= 21.4    The candle has a height of 21.4 cm after burning for 22 hours.

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step-by-step explanation:

a negative exponent is translated as follows:

so, we have