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

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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 slopeintercept form.
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 SlopeIntercept form. {For instance, I will use the first ordered pair (x, y) = (3, 110) where x = 3 and y = 110}
y = mx + b <SlopeIntercept Form>
110 = (25)(3) + b Substitute the slope and one of your ordered pairs
110 = 75 + b Solve for 'b', the yintercept value
110 = 75 + b
75 75
35 = b
b = 35
With the slope 'm' and yintercept '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 SlopeIntercept form.
y = mx + b <SlopeIntercept form>
y = 25x + 35 Only substitute the values of m and b to get your equation
SOLUTION: y = 25x + 35
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