Question

The graph shows the relationship between the United States dollar and the euro, the currency of the European Union, in December 2011. Part B: Justify why the relationship shown in the graph is a proportional relationship.

Answer 1

Explanation:

Let the equation of the line representing relation between the euros and dollars is,

E = mD + b

Where 'E' = Number of euros

D = Number of dollars

m = slope of the line

b = y-intercept

Slope of a line which passes through two points (120, 90) and (400, 300) will be,

m =
`(y_2-y_1)/(x_2-x_1)` =
`(300-90)/(400-120)`

m = 0.75

Equation of the line passing through (120, 90),

90 = 0.75(120) + b

b = 90 - 90 = 0

Therefore, equation of the line will be,

E = mD

E ∝ D

Here m = Proportionality constant

And the relation between the numbers of Euros and US dollars is a proportional relationship.