Question

The graph shows the total distance a tour group traveled as a function of time measure in days. What is the rate of change?

A) 35 miles per day

B) 25 miles per day

C) 50 miles per day

D) 35 miles per hour

Answer 1

Answer:

Option A is correct

35 miles per day

Step-by-step explanation:

Using slope formula:

$\text{Slope (m)} = \frac{y_2-y_1}{x_2-x_1}$        ....[1]

From the given graph:

Here, y represents the distance in miles and x represents the time in days

Consider two points i.e

(2, 70) and (4, 140)

then;

Substitute these in [1] we have;

$m = \frac{140-70}{4-2} = \frac{70}{2} = 35$

Therefore, the rate of change or slope of the given line is, 35 miles per day

Answer 2

The rate of change is 35 miles per day.

A linear equation is in the form:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept.

Let y represent the distance in mile and x represent the years.

From the graph we can see that the line passes through the point (0,0) and  (5, 175). Hence:

$slope(m)=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{175-0}{5-0} \\\\m=35\ miles\ per\ hour$

Hence the rate of change is 35 miles per day.

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