Question

A. The point (3.5, 210) is on the graph. Explain what this means in terms of the car.

Answer 1

Answer/Step-by-step explanation:

A. The point (3.5, 210) on the graph means the car travelled a distance of 210 miles, at constant speed, for 3.5 hours.

B. To find out if the point (1, 60) is on the line, first, calculate the slope of the line (rate of change), and then find the rate of change between the point (1, 60) and the point (3.5, 210). If you get the same value as the slope of the line, it definitely means (1, 60) is a point of the graph.

Calculating slope of the line using (3.5, 210) and (5, 300):

$slope(m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{300 - 210}{5 - 3.5}$

$slope(m) = \frac{90}{1.5}$

$slope(m) = 60$

Calculating the rate of change (slope) between (1, 60) and (3.5, 210):

$= \frac{y_2 - y_1}{x_2 - x_1} = \frac{210 - 60}{3.5 - 1}$

$= \frac{150}{2.5} = 60$

Rate of change (slope) = 60

Since the average rate of change between (1, 60) and the given point on the graph, (3.5, 210), is the same as the slope of the graph, therefore the point (1, 60) is a point on the graph also.

The answer is, YES.