The difference between consecutive y-values of a linear function is constant, given that the x-value differences are also constant
The athlete that maintained a consistent speed is the runner
The equation that represents the runner's distance as a function of time is y = 187.5·x
The reason the above values are correct are as follows:
The given data are;
The distance and time of the runner, the biker, and the swimmer
Required:
To find the athlete that maintained a consistent speed
To write an equation for the athlete
Solution:
The athlete that maintains a consistent speed is one that has a constant common difference between the x values and a constant common difference between the y values simultaneously
From the given data, the common difference between the time values of all the athletes are constant, therefore, the athlete required will be the athlete that has a constant common difference between the y-values
For the Runner, we have;
937.5 - 375 = 562.5
1,500 - 937.5 = 562.5
2062.5 - 1,500 = 562.5
2625 - 2062.5 = 562.5
3,187.5 - 2625 = 562.5
3,750 - 3,187.5 = 562.5
Therefore, the common difference between the y-value for the runner is constant and therefore the distance to time of the runner has a straight line relationship
The slope of the straight line graph, m = 562.5/3 = 187.5
The equation is y - 375 = 187.5(x - 2)
y = 187.5·x - 375 + 375 = 187.5·x
The equation that represent the athletes distance as a function of time is therefore, y = 187.5·x
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