Deciding Whether a Relationship Is Proportional

Question 1

x values 2, 4, 6 match y values 5, 10, 15. Is y proportional to x?

Accepted Answer

Yes, because each y/x ratio is 2.5.

Answer

Yes, because each x value is less than its y value.

Answer

No, because the y/x ratios are 2.5, 2.5, and 3.

Answer

No, because the table does not include (0, 0).

Question 2

For ordered pairs (1, 3), (2, 7), and (3, 9), is y proportional to x?

Accepted Answer

No, because the y/x ratios are not all equal.

Answer

Yes, because each y value is greater than its x value.

Answer

Yes, because the x-values increase by 1.

Answer

No, because the y-values are not all even numbers.

Question 3

A table pairs x values 3, 5, 8 with y values 12, 20, 32. Is the relationship proportional?

Accepted Answer

Yes, because each y/x ratio is 4.

Answer

Yes, because the y-values are larger than the x-values.

Answer

No, because the x-values do not increase by the same amount.

Answer

No, because the y/x ratios fall from 4 to 3.75.

Question 4

x values 2, 4, 6 match y values 8, 12, 16. Does the table show a proportional relationship?

Accepted Answer

No, because the y/x ratios are 4, 3, and 8/3.

Answer

Yes, because y increases by 4 each row.

Answer

Yes, because x increases by 2 each row.

Answer

No, because proportional tables cannot have even numbers.

Question 5

A table gives (4, 6), (8, 12), and (12, 18). Is y proportional to x?

Accepted Answer

Yes, because each y/x ratio is 1.5.

Answer

Yes, because each ordered pair has positive numbers.

Answer

No, because the y/x ratio changes from 1.5 to 1.6.

Answer

No, because x and y increase by different amounts.

Question 6

A table shows x values 5, 10, 15 and y values 15, 30, 50. Is y proportional to x?

Accepted Answer

No, because the y/x ratios are not all 3.

Answer

Yes, because 15 and 30 both match a ratio of 3.

Answer

Yes, because both columns increase.

Answer

No, because y is greater than x in every row.

Question 7

x values 0.5, 1, 1.5 match y values 2, 4, 6. Is y proportional to x?

Accepted Answer

Yes, because each y/x ratio is 4.

Answer

Yes, because the y-values are whole numbers.

Answer

No, because x-values include decimals.

Answer

No, because the y/x ratios are 4, 4, and 3.

Question 8

For (1, 2), (2, 4), and (4, 7), does the table show y proportional to x?

Accepted Answer

No, because the ratios are 2, 2, and 1.75.

Answer

Yes, because the first two rows have the same ratio.

Answer

Yes, because y increases as x increases.

Answer

No, because x skips from 2 to 4.

Question 9

A table pairs 2 meters with 6 seconds, 5 meters with 15 seconds, and 9 meters with 27 seconds. Is time proportional to distance?

Accepted Answer

Yes, because each seconds-per-meter ratio is 3.

Answer

Yes, because the distances are in meters.

Answer

No, because 2, 5, and 9 are not equally spaced.

Answer

No, because the seconds-per-meter ratios are 3, 3, and 2.7.

Question 10

A table shows x values 3, 6, 9 and y values 10, 20, 27. Is y proportional to x?

Accepted Answer

No, because the y/x ratios are 10/3, 10/3, and 3.

Answer

Yes, because the first two rows have the same ratio.

Answer

Yes, because x increases by 3 each row.

Answer

No, because y-values must increase by 10 every row.

Question 11

A table lists (6, 4), (9, 6), and (12, 8). Is y proportional to x?

Accepted Answer

Yes, because each y/x ratio is 2/3.

Answer

Yes, because each x/y ratio is 2/3.

Answer

No, because y is smaller than x in every row.

Answer

No, because the y-values increase by 2.

Question 12

x values 2, 5, 8 match y values 6, 15, 25. Does this table show proportionality?

Accepted Answer

No, because 25/8 is not equal to 6/2 or 15/5.

Answer

Yes, because the first two ratios are equal.

Answer

Yes, because each x value has one y value.

Answer

No, because x-values and y-values are both increasing.

Question 13

A table gives x values 7, 14, 21 and y values 1, 2, 3. Is y proportional to x?

Accepted Answer

Yes, because each y/x ratio is 1/7.

Answer

Yes, because each y-value is less than 10.

Answer

No, because y is less than x in every row.

Answer

No, because the y/x ratios are 1/7, 1/7, and 1/8.

Question 14

A table pairs x values 4, 8, 12 with y values 10, 18, 30. Is y proportional to x?

Accepted Answer

No, because the y/x ratios are 2.5, 2.25, and 2.5.

Answer

Yes, because two rows have a ratio of 2.5.

Answer

Yes, because the largest x matches the largest y.

Answer

No, because proportional tables must start with x = 1.

Question 15

A straight line goes through (0, 0) and (4, 12). Does the graph show y proportional to x?

Accepted Answer

Yes, because it is a straight line through the origin.

Answer

Yes, because the point (4, 12) has positive coordinates.

Answer

No, because the line does not pass through the origin.

Answer

No, because y is greater than x at (4, 12).

Question 16

A line passes through (0, 2) and (3, 8). Does this graph represent a proportional relationship?

Accepted Answer

No, because the line does not pass through (0, 0).

Answer

Yes, because the line is straight.

Answer

Yes, because y increases when x increases.

Answer

No, because proportional graphs cannot have positive points.

Question 17

A graphed line passes through (0, 0) and (5, 2). Is y proportional to x?

Accepted Answer

Yes, because the line passes through the origin.

Answer

Yes, because 5 is greater than 2.

Answer

No, because the unit rate is less than 1.

Answer

No, because the line misses the origin.

Question 18

A line crosses the y-axis at 6 and passes through (2, 10). Is it proportional?

Accepted Answer

No, because the y-intercept is 6, not 0.

Answer

Yes, because the line has a constant rate of change.

Answer

Yes, because 10 is greater than 6.

Answer

No, because a proportional graph must cross the x-axis at 6.

Question 19

A straight graph contains (0, 0), (2, 7), and (4, 14). Is y proportional to x?

Accepted Answer

Yes, because the straight line goes through the origin.

Answer

Yes, because the y-values are odd and even.

Answer

No, because 7 is not a multiple of 2.

Answer

No, because the line crosses the y-axis above the origin.

Question 20

A line goes through (1, 4) and (2, 7). Does the graph show y proportional to x?

Accepted Answer

No, because the line would cross the y-axis at 1, not 0.

Answer

Yes, because both ordered pairs have positive coordinates.

Answer

Yes, because the line is straight.

Answer

No, because proportional graphs cannot pass through (1, 4).

Question 21

A ray starts at the origin and passes through (6, 9). Does the graph show proportionality?

Accepted Answer

Yes, because every point on the ray follows one constant ratio.

Answer

Yes, because 9 is greater than 6.

Answer

No, because a ray is not a full line.

Answer

No, because the origin has coordinates of zero.

Question 22

A line crosses the y-axis at -3 and contains (2, 5). Does y vary proportionally with x?

Accepted Answer

No, because the graph does not pass through the origin.

Answer

Yes, because it is a straight line.

Answer

Yes, because the line includes the point (2, 5).

Answer

No, because proportional graphs cannot have negative numbers anywhere.

Question 23

A graphed line passes through (0, 0) and (8, 4). Is y proportional to x?

Accepted Answer

Yes, because the line is straight and passes through (0, 0).

Answer

Yes, because x is twice y at one point.

Answer

No, because the graph goes upward too slowly.

Answer

No, because the y/x ratio changes from 0.5 to 1.

Question 24

A straight line passes through (0, 5) and (5, 0). Is y proportional to x?

Accepted Answer

No, because the line does not pass through the origin.

Answer

Yes, because the line crosses both axes.

Answer

Yes, because the two points use the same numbers.

Answer

No, because proportional graphs must be horizontal.

Question 25

A line through the origin also passes through (3, 1.5). Does it model a proportional relationship?

Accepted Answer

Yes, because it has the form y = kx with k = 0.5.

Answer

Yes, because 3 is a whole number.

Answer

No, because 1.5 is a decimal.

Answer

No, because proportional graphs cannot go through (3, 1.5).

Question 26

A graph line crosses (0, 1) and (4, 9). Is this relationship proportional?

Accepted Answer

No, because the line has y-intercept 1 instead of 0.

Answer

Yes, because the line rises from left to right.

Answer

Yes, because 9 - 1 equals 8.

Answer

No, because proportional graphs cannot include (4, 9).

Question 27

A graph is a straight line through (0, 0), (10, 25), and (20, 50). Is y proportional to x?

Accepted Answer

Yes, because the points lie on a straight line through the origin.

Answer

Yes, because the y-values are greater than the x-values.

Answer

No, because the x-values skip by 10.

Answer

No, because the line meets the y-axis at 25 instead of the origin.

Question 28

The equation y = 4x describes a relationship. Is y proportional to x?

Accepted Answer

Yes, because it is in the form y = kx.

Answer

Yes, because 4 is greater than 1.

Answer

No, because x is a variable.

Answer

No, because y = 4x is not in the form y = kx.

Question 29

The equation y = 3x + 2 describes a relationship. Is y proportional to x?

Accepted Answer

No, because the equation is not in the form y = kx.

Answer

Yes, because x is multiplied by 3.

Answer

Yes, because 2 is a constant number.

Answer

No, because proportional equations cannot include multiplication.

Question 30

If y = x/5, is y proportional to x?

Accepted Answer

Yes, because y equals 1/5 times x.

Answer

Yes, because division always makes y smaller.

Answer

No, because proportional relationships cannot use fractions.

Answer

No, because x is divided instead of multiplied.

Question 31

The equation y = 2(x + 3) describes a relationship. Is y proportional to x?

Accepted Answer

No, because it expands to y = 2x + 6, not y = kx.

Answer

Yes, because x is multiplied by 2.

Answer

Yes, because parentheses can be removed.

Answer

No, because proportional equations cannot use variables.

Question 32

A gym charges $10 to join plus $6 per class. Let y be the cost in dollars for x classes. Is y proportional to x?

Accepted Answer

No, because y = 6x + 10, not y = kx.

Answer

Yes, because each class costs $6.

Answer

No, because the price of each class changes as x grows.

Answer

Yes, because the cost increases with the number of classes.

Question 33

A recipe uses 12 grams of spice for each batch. Let y be the grams of spice for x batches. Is y proportional to x?

Accepted Answer

Yes, because y = 12x.

Answer

Yes, because grams are metric units.

Answer

No, because batches and grams are different units.

Answer

No, because 12 grams per batch is a rate, not a ratio.

Question 34

A taxi costs $4 to start plus $2 per kilometer. Let y be the cost in dollars for x kilometers. Is y proportional to x?

Accepted Answer

No, because y = 2x + 4, not y = kx.

Answer

Yes, because each kilometer adds $2.

Answer

No, because each kilometer costs a different amount.

Answer

Yes, because y increases at a constant rate of $2 per kilometer.

Question 35

Rule: y is 7 more than twice x. Is y proportional to x?

Accepted Answer

No, because the rule is y = 2x + 7.

Answer

Yes, because the rule says twice x.

Answer

Yes, because 7 is a constant.

Answer

No, because twice x is never proportional.

Question 36

Rule: y is 0.75 times x. Is y proportional to x?

Accepted Answer

Yes, because y = 0.75x.

Answer

Yes, because 0.75 is less than 1.

Answer

No, because decimals cannot be constants of proportionality.

Answer

No, because y is always less than x.

Question 37

The equation y - 5 = 2x describes a relationship. Is y proportional to x?

Accepted Answer

No, because it rewrites as y = 2x + 5.

Answer

Yes, because x is multiplied by 2.

Answer

Yes, because subtracting 5 makes the start 0.

Answer

No, because k must equal 5.

Question 38

If y/3 = x, is y proportional to x?

Accepted Answer

Yes, because the equation rewrites as y = 3x.

Answer

Yes, because x is alone on one side.

Answer

No, because y is divided by 3.

Answer

No, because proportional equations cannot be rewritten.

Question 39

For every 1 liter of juice, there are 4 liters of water; water y for juice x. Is y proportional to x?

Accepted Answer

Yes, because y = 4x.

Answer

Yes, because water is measured in liters.

Answer

No, because 4 liters is more than 1 liter.

Answer

No, because y = 4x does not pass through the origin.

Question 40

The equation 2y = 8x describes a relationship. Is y proportional to x?

Accepted Answer

Yes, because it simplifies to y = 4x.

Answer

Yes, because both sides have even coefficients.

Answer

No, because y is not alone at first.

Answer

No, because 8x is greater than 2y.

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Deciding Whether a Relationship Is Proportional

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Deciding Whether a Relationship Is Proportional

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner