Question

What is the constant speed of freddy and sam?

Answer 1

The constant speed, or "average rate of change" is their slope.

so  hmmm looking at Fred's graph, let's pick two points on the line, say 0,0 the origin and 8,2

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 0}}\quad ,&{{ 0}})\quad % (c,d) &({{8}}\quad ,&{{ 2}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{2-0}{8-0}\implies \cfrac{2}{8}\implies \cfrac{1}{4}$

now, for Sam, let's use the last two points in the table then,

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 20}}\quad ,&{{ 2\frac{1}{2}}})\quad % (c,d) &({{32}}\quad ,&{{ 4}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{4-2\frac{1}{2}}{32-20}\implies \cfrac{4-\frac{5}{2}}{32-20} \\\\\\ \cfrac{\quad \frac{8-5}{2}\quad }{12}\implies \cfrac{\quad \frac{3}{2}\quad }{\frac{12}{1}}\implies \cfrac{3}{2}\cdot \cfrac{1}{12}\implies \cfrac{1}{8}$

Answer 2

Answer:

The constant speed of Freddy is o.25 miles per minute

Constant speed of Sam is 0.125 miles per minute

Step-by-step explanation:

To find the constant speed , find out the slope using any two points

Fast  Freddy:

(4,1) (8,2)

To find slope apply slope formula

$slope = \frac{y_2-y_1}{x_2-x_1} =\frac{2-1}{8-4} =\frac{1}{4}=0.25$

Constant speed is 1/4

Speedy Sam:

(4,0.5) and (32,4)

$slope = \frac{y_2-y_1}{x_2-x_1} =\frac{4-0.5}{32-4} =0.125$

The constant speed of Freddy is o.25 miles per minute

Constant speed of Sam is 0.125 miles per minute