Proportional Relation Line

The graph shown is:

• linear function but not proportional.

• function, but not linear or proportional.

• proportional function.

• Not a function, linear or proportional.

Which of the tables shows a proportional relationship?

• A and B only

• B and C only

• A, B and C

• none of them

The table shown is:

• Proportional, because it is going up by 2 each time.

• Linear, because it is going up by two each time.

• Not a function, because 1 appears in the table twice.

• A function but non linear, because it doesn't start at zero.

Is this a function? 

• Yes

• No

The number of trees and the number of apples are given in the table above.  Determine which statement below is correct.

• The table is not proportional because the unit rate is not constant.

• The table is proportional and the unit rate is 1/13

• The table is proportional and the unit rate is 13.

• The table is not proportional because it doesn't pass through the origin.

quantities that have a constant ratio

• rate of change

• equivalent ratios

• intercepts

• proportional

• slope

Answer explanation

Quantities are proportional if they have a constant ratio. The constant of proportionality is found by the ratio: y/x.

The rate of change is how one quantity changes in relation another. The slope is equal to the rate of change. x- and y-intercepts occur for straight lines as well as other relationships. Equivalent ratios are ratios that simplify to the same value.

a relationship that produces a straight line when graphed

• rate of change

• equivalent ratios

• axis

• slope

• linear

Answer explanation

A linear relationship produces a straight line when graphed. The rate of change is how one quantity changes in relation another. If the rate of change is constant, a straight line will be produced when graphed, but the rate of change of some relationships are not constant, so will not produce a straight line. The slope is equal to the rate of change, so will only produce a straight line when it is constant. An axis is a number line in a coordinate system.

a linear relationship that intersects the origin

• rate of change

• equivalent ratios

• intercepts

• slope

• proportional

Answer explanation

Quantities are proportional if they have a constant ratio. When we graph a proportional relationship produces a straight line that intersects the origin.

The rate of change is how one quantity changes in relation another, and that relationship may or may not be proportional. If the rate of change is constant, a straight line will be produced when graphed, but the line will only intersect the origin if the relationship is also proportional. The slope is equal to the rate of change. x- and y-intercepts occur for straight lines as well as other relationships.

equal to the rate of change ( Δy/Δx )

• linear

• equivalent ratios

• intercepts

• slope

• proportional

Answer explanation

The slope is equal to the rate of change ( Δy/Δx ).

If the slope is constant, the relationship will be linear. If the slope is constant and the graph intersects the origin, it is a proportional relationship. x- and y-intercepts occur for straight lines as well as other relationships.

ratios that simplify to the same value

• linear

• equivalent ratios

• intercepts

• slope

• constant

Answer explanation

Equivalent ratios are ratios that simplify to the same value.

The slope is equal to the rate of change ( Δy/Δx ). Linear relationships produce a straight line when graphed.

x- and y-intercepts are where the graph crosses the x- and y-axes. Constant means "not changing".