Algebraic Representations of Two-Variable Relationships

Algebraic Representations of Two-Variable Relationships

Independent Variable

• a variable whose value determines the value of the dependent variable

• x value in an equation, table, and graph

• time (minutes, hours, days, weeks)

Dependent Variable

• a variable whose value depends on the value of the independent variable

• y value in an equation, table, or graph

• this value changes

Multiplicative Relationship y = ax

• The independent and dependent variable are said to have a multiplicative relationship when you multiply any x-value times the SAME number to get the y value

• If it is not the same number every time, it is NOT a multiplicative relationship

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Additive Relationship y = x + a

• The independent and dependent variable are said to have an additive relationship when you add the SAME number to any x-value to get the y value

• If it is not the same number every time, it is NOT an additive relationship

Coordinate Plane

Origin (0,0)

A point is located on the x axis when the y value in the ordered pair is 0

A point is located on the y axis when the x value is the ordered pair is 0

Multiple Choice

On a graph, which axis shows the dependent variable?

• x-axis

• y-axis

• neither

• it changes

Multiple Choice

Eduardo had eight dollars, then he started to save a dollar a week. Which equation can be used to find how much money Eduardo will have at the end of the month?

• y = 1 + 8

• y = 8x

• y = x + 8

• y = ⁸/_x

Multiple Choice

Is the picture showing an additive or a multiplicative relationship?

• Additive
• Multiplicative

Multiple Choice

On a graph, which axis shows the independent variable?

• x-axis
• y-axis
• neither
• it changes

Multiple Choice

What is (0,0) known as?

• The origin
• The intersector
• It is just an ordered pair
• None of the above

Multiple Choice

What makes up an ordered pair?

• Two random numbers
• An x-value and a y-value
• Two pears
• Two lines

Multiple Choice

How many quadrants are on the coordinate plane?

• 1
• 2
• 3
• 4

Multiple Choice

Each day, Kellan swam a different number of laps and then his time was recorded. The amount of time it takes Kellan to swim his required number of laps varies, as shown in the table.

What is the independent quantity in this situation?

• The time it takes to swim one lap

• The distance of one lap in the swimming pool

• The number of minutes

• The number of laps

Multiple Choice

Each day, Kellan swam a different number of laps and then his time was recorded. The amount of time it takes Kellan to swim his required number of laps varies, as shown in the table.

What is the independent quantity in this situation?

• The time it takes to swim one lap

• The distance of one lap in the swimming pool

• The number of minutes

• The number of laps