Question

Determine whether or not the equation shows a proportional relationship. If it does, identify the unit rate (constant of proportionality).

y =25x, a = 5x + 5, m = 105.25n

Answer 1

y = 25·x shows a proportional relationship

a = 5·x + 5 does not show a proportional relationship

m = 105.25·n shows a proportional relationship

Explanation:

An equation that shows a proportional relationship is of the form, y = kx

Where;

k = The constant of proportionality = y/x

Therefore, the equation, y = 25·x shows a proportional relationship

The constant of proportionality = k = y/x = 25

Similarly, the equation m = 105.25·n shows a proportional relationship

The constant of proportionality = k = m/n = 105.25

When the equation shows a proportional relationship, the graph of the equation passes through the origin, therefore, the equation of the form, y = m·x + c, where c = the y-intercept > 0, the equation does not show a proportional relationship

The equation a = 5·x + 5, which is of the form, y = m·x + c, with c = 5 > 0, therefore, does not show a proportional relationship.

Therefore;

y = 25·x shows a proportional relationship

m = 105.25·n shows a proportional relationship

a = 5·x + 5 does not show a proportional relationship.