Question

I didn't know how to do this "Who, if anyone, traveled at a aster speed? Explain."

Answer 1

Given:

The graph shows the relationship between the total distance Dominique traveled and the time.

The distance Ella traveled after x hours is represented by the equation,

$y=550x..........\left(1\right)$

To find out: who traveled at a faster speed if anyone.

Explanation:

Let us find the equation of the line for Dominique.

Consider two points,

$\lparen0,0),\left(2,1100\right)$

Using the two-point formula,

$\begin{gathered} \frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1} \\ \frac{y-0}{1100-0}=\frac{x-0}{2-0} \\ \frac{y}{1100}=\frac{x}{2} \\ y=\frac{1100}{2}x \\ y=550x..........\left(2\right) \end{gathered}$

It is of the form,

$y=mx+c,\text{ where m is the slope.}$

Since the slope (i.e. speed) of the equation is m = 550 which is equivalent to the slope (i.e speed) of the equation Ella's.

Therefore, both traveled at the same speed.

Final answer:

Both traveled at the same speed.