Example 2 EXERCISE Carlos is jogging at a constant speed. He starts a timer when he is
12 feet from his starting position. After 3 seconds, Carlos is 21 feet from his
starting position. Write a linear equation to represent the distance d of Carlos
from his starting position after t seconds.

The linear equation used to represent Carlos distance (d) from his starting position after t seconds is d = 3t + 12

A linear equation is given by:

y = mx + b;

where y, x are variables, m is the rate of change and b is the y intercept.

Let d represent Carlos distance from his starting position after t seconds.

Given that He starts a timer when he is  12 feet from his starting position, hence b = 12 feet. After 3 seconds, Carlos is 21 feet from his starting position. Therefore:

21 = 3m + 12

3m = 9

m = 3 ft per second

The linear equation used to represent Carlos distance (d) from his starting position after t seconds is d = 3t + 12

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Step-by-step explanation:

Given

Represent time with t and distance with d

The time at which he sets his timer is 0.

So:

After 3 seconds:

Required

Determine the linear equation

First, we need to determine the slope (m):

Substitute in, values

Next, we determine the equation sing

Where

Add 11 to both sides

Hence, the linear equation is:

step-by-step explanation:

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step-by-step explanation: