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?

Answer:  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     y2Now we put these into the equation and solve[tex]\frac{22-17.5}{24-9}[/tex]   =[tex]\frac{3}{10}[/tex]Now that we have the slope of 3/10 we can use this to find the y-intercept using the point-slope equation.[tex]y-y_{1} =m(x-x_{1} )[/tex]                 y-17.5= .3(x-9) Solvey-17.5=.3x-2.7                                        y  -14.8=      .3x  +2.7         +2.7                                         +14.8               +14.8y=.3x+14.8                     the y-intercept is 14.8Now we use this equation to  plug in the 22 hours.y=.3(22) +14.8y=6.6+14.8y= 21.4    The candle has a height of 21.4 cm after burning for 22 hours.