Linear Relationships

At what point is the line crossing the Y-axis?

• 1.5

• -2

• 3

• -3

If the table is proportional, then what is the constant of proportionality?

• $15.50 per hour

• 15.5 hours per dollar

• $1.50 per hour

• 1.50 hours per dollar

If the table is constant, using k, find the total amount earned if you worked for 15 hours.

• $232.50

• $30.50

• $0.50

• $225

At what rate did the rain fall?

• 2 cm per hour

• ¹/₄ cm per hour

• ¹/₂ cm per hour

• 4 cm per hour

Which ordered pair represents the origin on a graph?

• (1,1)

• (0,1)

• (0,0)

• (1,0)

Does the table above represent a proportional or non-proportional relationship?

• Proportional

• Non-Proportional

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.