Linear Relationships - Vocabulary

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.

Tags

CCSS.HSG.SRT.A.2

CCSS.HSG.SRT.A.3

how one quantity changes in relation to another quantity

• rate of change

• equivalent ratios

• constant

• proportional

• linear

Answer explanation

The rate of change is how one quantity changes in relation another ( Δy/Δx ).

Although a proportional relationship and a linear relationship are two ways that quantities may change in relation to each other, there are other ways. Equivalent ratios and are static (not changing). Constant means "not changing".

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.B.6

CCSS.HSS.ID.C.7

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.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSS.ID.C.7

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.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSS.ID.C.7

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.

Tags

CCSS.HSF.IF.B.6

CCSS.HSS.ID.C.7

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".

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.3

means "not changing"

• linear

• equivalent ratios

• intercepts

• slope

• constant

Answer explanation

Constant means "not changing".

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.

Tags

CCSS.HSS.ID.C.7

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".

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

CCSS.HSS.ID.C.7

a number line in a coordinate system

• axis

• equivalent ratio

• intercept

• slope

• linear

Answer explanation

The number lines in a coordinate system are the axes. (The singular of axes is is axis).

A linear relationship produces a straight line when graphed. The slope is equal to the rate of change. Intercepts are where the graphed relationship crosses an axis. Equivalent ratios simplify to the same value.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

equal to the slope ( Δy/Δx )

• linear

• equivalent ratios

• intercepts

• rate of change

• constant

Answer explanation

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

Constant means "not changing". If the slope is constant, the relationship will be linear. Equivalent ratios simplify to the same value. Intercepts are where a graph crosses an axis.

Tags

CCSS.HSS.ID.C.7