exercise carlos is jogging at a constant speed. he starts a timer when he is 12 feet from his starting…

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.

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.

Answer

Explanation:

Step1: Find the slope

The slope $m$ of a linear equation $d = mt + b$ (where $d$ is distance and $t$ is time) is given by the formula $m=\frac{\Delta d}{\Delta t}$. We have two - points: $(t_1,d_1)=(0,12)$ (at $t = 0$ seconds, $d = 12$ feet) and $(t_2,d_2)=(3,21)$. Then $m=\frac{d_2 - d_1}{t_2 - t_1}=\frac{21 - 12}{3-0}=\frac{9}{3}=3$.

Step2: Find the y - intercept

The y - intercept $b$ is the value of $d$ when $t = 0$. We know that when $t = 0$, $d = 12$, so $b = 12$.

Step3: Write the linear equation

The linear equation in slope - intercept form is $d=mt + b$. Substituting $m = 3$ and $b = 12$, we get $d = 3t+12$.

Answer:

$d = 3t + 12$