Functions and Linear Relationships Vocabulary Words

Which of the statements about the graph below is true?

• The graph is proportional and has an equation of y = -x +18.

• The graph is non-proportional and has an equation of y = -x + 18.

• The graph is non-proportional and has an equation of y = -2x + 18.

• None of the above statements are true.

The table below shows the amount that a catering company charges based on the number of people at an event. Which of the following equations shows the relationship between c, the amount the company charges based on p, the number of people at the event?

• c = 16p

• c = 75p + 13

• p = 13c + 75

• c + 13p + 75

Zane owes his dad money for his cell phone that he lost. So far, Zane has paid his dad $23, and he will pay his dad an additional $45 each month until he had repaid him for the phone. Which equation shows the relationship between m, the number of months that Zane has been making payments and t, the total amount he has paid his dad?

• t = 45m + 23

• m = 45t + 23

• t = 23m + 45

• t = 68m

Preston needs to write an equation in slope-intercept form to represent the relationship between x and y in the table below. What will be the value of the y-intercept in this equation?

• 12

• -6

• -12

• -15

The diagram shows a linear function of g. What is the value of k.

• 5

• 4

• 7

• 8

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.

Points where a graphed relationship crosses an axis.

• linear

• equivalent ratios

• intercepts

• slope

• constant

Answer explanation

Intercepts are points where a graph crosses an axis.

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.

Constant means "not changing".