Question

An atlas contains a map of Ohio. The table shows data from the key on the map.

a. Graph the data.
b. Find the slope of the line through the data points. What does this mean in the context of the problem?
c. The map distance between Toledo and Columbus is 48 millimeters. What is the actual distance?
d. Cincinnati is about 225 miles from Cleveland. What is the distance between these cities on the map?

Answer 1

The answer is below

Explanation:

a) The graph is attached

b) The table shows a linear relationship between x and y.

A linear equation is in the form y = mx + b, where y is a dependent variable, x is an independent variable, m is the rate of change (slope) and b is the value of y when x = 0.

x represent the distance on map in mm and y represent the actual distance in mile. The table (x, y) has the points (10, 25) and (20, 50). The equation is given by:

`y-y_1=(y_2-y_1)/(x_2-x_1) (x-x_1)\\\\y-25=(50-25)/(20-10) (x-10)\\\\y-25=2.5(x-10)\\\\y-25=2.5x-25\\\\y=2.5x`

The slope m = 2.5. This means that for every 1 mm on the map, the actual distance increases by 2.5 miles.

c) y = 2.5x

put x = 48 mm

y = 2.5(48)

y = 120 miles

The actual distance between Toledo and Columbus is 120 miles

d) y = 2.5x

Put y = 225 miles

225 = 2.5x

x = 225/2.5

x = 90 mm

The distance on map between Cincinnati and Cleveland is about 90 mm.