Mathematics
After 3 minutes an ant traveled 110 meters and after 8 minutes the ant

Question Description

After 3 minutes an ant traveled 110 meters and after 8 minutes the ant will have traveled 235 meters. Assuming a linear equation can be used to model the change in distance traveled over time between 3 and 8 minutes. Write in slope-intercept form.

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Final Answer

Let  'x' represent the time in minutes  and 'y' represent the distance in meters.  Use this concept to get your ordered pairs.

            "After 3 minutes, an ant traveled 110 meters"  >>>>>   (x, y) = (3, 110)

            "After 8 minutes, the ant will have traveled 235 meters"   >>>>>>  (x, y) = (8, 235)

Calculate the slope  {Let  (x1, y1) = (3, 110)   and  (x2, y2) = (8, 235) for using the slope formula}

                                     m = (y2 - y1)/(x2 - x1)             <Slope Formula>

                                     m = (235 - 110)/(8 - 3)

                                     m =  125/5

                                     m = 25

Substitute the slope and one of your ordered pairs into the Slope-Intercept form.   {For instance, I will use the first ordered pair (x, y) = (3, 110) where x = 3 and y = 110}

                                     y = mx + b                         <Slope-Intercept Form>

                                  110 = (25)(3) + b              Substitute the slope and one of your ordered pairs

                                  110 = 75 + b                         Solve for 'b', the y-intercept value

                                  110 = 75 + b

                                   -75    -75

                                   35 = b

                                    b = 35

With the slope 'm' and y-intercept 'b' known, we can simply start back to the slope intercept form again and only substitute these values (leave x and y as they are).  This will get you your equation in Slope-Intercept form.

                                   y = mx + b                  <Slope-Intercept form>

                                   y = 25x + 35               Only substitute the values of m and b to get your equation


SOLUTION:           y = 25x + 35

Wallace H (1013)
University of Maryland

Anonymous
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