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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.

Respuesta :

MrRoyal

Answer:

[tex]d =\frac{10}{3}t + 11[/tex]

Step-by-step explanation:

Given

Represent time with t and distance with d

The time at which he sets his timer is 0.

So:

[tex](t_1,d_1) = (0,11)[/tex]

After 3 seconds:

[tex](d_2,d_2) = (3,21)[/tex]

Required

Determine the linear equation

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

[tex]m = \frac{d_2 - d_1}{t_2 - t_1}[/tex]

Substitute in, values

[tex]m = \frac{21 - 11}{3 - 0}[/tex]

[tex]m = \frac{10}{3}[/tex]

Next, we determine the equation sing

[tex]d - d_1 = m(t - t_1)[/tex]

Where

[tex](t_1,d_1) = (0,11)[/tex]

[tex]m = \frac{10}{3}[/tex]

[tex]d - 11 =\frac{10}{3}(t - 0)[/tex]

[tex]d - 11 =\frac{10}{3}t - 0[/tex]

[tex]d - 11 =\frac{10}{3}t[/tex]

Add 11 to both sides

[tex]d - 11+11 =\frac{10}{3}t + 11[/tex]

[tex]d =\frac{10}{3}t + 11[/tex]

Hence, the linear equation is: [tex]d =\frac{10}{3}t + 11[/tex]

raphealnwobi

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

Find out more at: https://brainly.com/question/13911928

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