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

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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.

Jul 27th, 2014

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

Jul 27th, 2014

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Jul 27th, 2014
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Jul 27th, 2014
Oct 20th, 2017
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