After 2 minutes an ant traveled 110 meters and after 7 minutes the ant will have traveled 260 meters. Assuming a linear equation can be used to model the change in distance traveled over time between 2 and 7 minutes, let y be the distance traveled (in meters) after x minutes and complete this linear model in slope-intercept form:

y = 30x + 50

Step-by-step explanation:

let y be the distance traveled (in meters) after x minutes.

If we plot y on the vertical axis and x on the horizontal axis, a straight line would be formed. The slope of the straight line would be

Slope, m = (260 - 110)/(7 - 2)

m = 150/5 = 30

The equation of the straight line can be represented in the slope-intercept form, y = mx + c

Where

c = intercept

m = slope

To determine the intercept, we would substitute x = 7, y = 260 and m = 30 into y = mx + c. It becomes

260 = 30 × 7 + c = 210 + c

c = 260 - 210

c = 50

The linear model becomes

y = 30x + 50