Linear Relationship Vocabulary

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.

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 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".

Where a line crosses the y-axis. The b value in y=mx+b.

• slope

• y-intercept

• origin

• equation

The steepness of a line. The m value in y=mx+b.

• slope

• y-intercept

• origin

• equation

Rise over Run

• slope

• y-intercept

• similar triangles

• linear function

What does it mean if an equation is written as y=mx

• The line passes through the origin

• The line has a zero slope

• It represents a proportional relationship

• The y-intercept is zero

The y value when x=0

• slope

• y-intercept

• origin

• equation