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Math Coach Amy
Amy Ferguson Moncure

7th Grade Math · Unit 5

Tables, Equations,
and Graphs

A table, an equation, and a graph can show the same relationship.

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Key Ideas Easy Medium Hard
What to Remember

Three views

A table, an equation, and a graph can show the same relationship.

Missing table value

On a proportional table, the missing value is the slope times x.

Level 1

Easy

Points and y = mx

Example
Find the slope, then write y = mx.
The points are (0, 0) and (1, 4).

m = change in ychange in x

m = 41

m = 41

m = 4

y = 4x

Answer: y = 4x

1
Find the slope, then write y = mx.
The points are (0, 0) and (2, 2).
Show Answer

m = change in ychange in x

m = 22

m = 22

m = 1

y = x

Answer: y = x

2
Find the slope, then write y = mx.
The points are (0, 0) and (2, 6).
Show Answer

m = change in ychange in x

m = 62

m = 62

m = 3

y = 3x

Answer: y = 3x

3
Find the slope, then write y = mx.
The points are (0, 0) and (3, 6).
Show Answer

m = change in ychange in x

m = 63

m = 63

m = 2

y = 2x

Answer: y = 2x

4
Find the slope, then write y = mx.
The points are (0, 0) and (4, 4).
Show Answer

m = change in ychange in x

m = 44

m = 44

m = 1

y = x

Answer: y = x

5
Find the slope, then write y = mx.
The points are (0, 0) and (1, 5).
Show Answer

m = change in ychange in x

m = 51

m = 51

m = 5

y = 5x

Answer: y = 5x

6
Find the slope, then write y = mx.
The points are (0, 0) and (3, 9).
Show Answer

m = change in ychange in x

m = 93

m = 93

m = 3

y = 3x

Answer: y = 3x

7
Find the slope, then write y = mx.
The points are (0, 0) and (4, 12).
Show Answer

m = change in ychange in x

m = 124

m = 124

m = 3

y = 3x

Answer: y = 3x

8
Find the slope, then write y = mx.
The points are (0, 0) and (5, 10).
Show Answer

m = change in ychange in x

m = 105

m = 105

m = 2

y = 2x

Answer: y = 2x

9
Find the slope, then write y = mx.
The points are (0, 0) and (2, 8).
Show Answer

m = change in ychange in x

m = 82

m = 82

m = 4

y = 4x

Answer: y = 4x

10
Find the slope, then write y = mx.
The points are (0, 0) and (6, 6).
Show Answer

m = change in ychange in x

m = 66

m = 66

m = 1

y = x

Answer: y = x

Level 2

Medium

The graph of y = mx

Example
Graph the proportional relationship.
y = x

y = x

The line passes through the origin because the equation is y = mx.

Another point is (1, 1).

The line continues in both directions through those points.

−112−112(0, 0)(1, 1)

Answer: through (0, 0) and (1, 1)

1
Graph the proportional relationship.
y = 2x
Show Answer

y = 2x

The line passes through the origin because the equation is y = mx.

Another point is (1, 2).

The line continues in both directions through those points.

−112−1123(0, 0)(1, 2)

Answer: through (0, 0) and (1, 2)

2
Graph the proportional relationship.
y = 3x
Show Answer

y = 3x

The line passes through the origin because the equation is y = mx.

Another point is (1, 3).

The line continues in both directions through those points.

−112−11234(0, 0)(1, 3)

Answer: through (0, 0) and (1, 3)

3
Graph the proportional relationship.
y = 4x
Show Answer

y = 4x

The line passes through the origin because the equation is y = mx.

Another point is (1, 4).

The line continues in both directions through those points.

−112−112345(0, 0)(1, 4)

Answer: through (0, 0) and (1, 4)

4
Graph the proportional relationship.
y = 12x
Show Answer

y = 12x

The line passes through the origin because the equation is y = mx.

Another point is (2, 1).

The line continues in both directions through those points.

−1123−112(0, 0)(2, 1)

Answer: through (0, 0) and (2, 1)

5
Graph the proportional relationship.
y = 13x
Show Answer

y = 13x

The line passes through the origin because the equation is y = mx.

Another point is (3, 1).

The line continues in both directions through those points.

−11234−112(0, 0)(3, 1)

Answer: through (0, 0) and (3, 1)

6
Graph the proportional relationship.
y = 14x
Show Answer

y = 14x

The line passes through the origin because the equation is y = mx.

Another point is (4, 1).

The line continues in both directions through those points.

−112345−112(0, 0)(4, 1)

Answer: through (0, 0) and (4, 1)

7
Graph the proportional relationship.
y = −x
Show Answer

y = −x

The line passes through the origin because the equation is y = mx.

Another point is (1, −1).

The line continues in both directions through those points.

−112−2−11(0, 0)(1, −1)

Answer: through (0, 0) and (1, −1)

8
Graph the proportional relationship.
y = −2x
Show Answer

y = −2x

The line passes through the origin because the equation is y = mx.

Another point is (1, −2).

The line continues in both directions through those points.

−112−3−2−11(0, 0)(1, −2)

Answer: through (0, 0) and (1, −2)

9
Graph the proportional relationship.
y = −12x
Show Answer

y = −12x

The line passes through the origin because the equation is y = mx.

Another point is (2, −1).

The line continues in both directions through those points.

−1123−2−11(0, 0)(2, −1)

Answer: through (0, 0) and (2, −1)

10
Graph the proportional relationship.
y = −32x
Show Answer

y = −32x

The line passes through the origin because the equation is y = mx.

Another point is (2, −3).

The line continues in both directions through those points.

−1123−4−3−2−11(0, 0)(2, −3)

Answer: through (0, 0) and (2, −3)

Level 3

Hard

A missing table value

Example
The table shows a proportional relationship. Find the missing books.
studentsbooks
15
2?
315
420

In a proportional relationship, every pair uses the same ratio.

books = 5 × students

books = 5 × 2

books = 10

Answer: 10

1
The table shows a proportional relationship. Find the missing miles.
hoursmiles
26
4?
618
824
Show Answer

In a proportional relationship, every pair uses the same ratio.

miles = 3 × hours

miles = 3 × 4

miles = 12

Answer: 12

2
The table shows a proportional relationship. Find the missing dollars.
ticketsdollars
14
28
312
4?
Show Answer

In a proportional relationship, every pair uses the same ratio.

dollars = 4 × tickets

dollars = 4 × 4

dollars = 16

Answer: 16

3
The table shows a proportional relationship. Find the missing minutes.
lapsminutes
3?
612
918
1224
Show Answer

In a proportional relationship, every pair uses the same ratio.

minutes = 2 × laps

minutes = 2 × 3

minutes = 6

Answer: 6

4
The table shows a proportional relationship. Find the missing pencils.
boxespencils
112
224
3?
448
Show Answer

In a proportional relationship, every pair uses the same ratio.

pencils = 12 × boxes

pencils = 12 × 3

pencils = 36

Answer: 36

5
The table shows a proportional relationship. Find the missing pages.
dayspages
210
4?
630
840
Show Answer

In a proportional relationship, every pair uses the same ratio.

pages = 5 × days

pages = 5 × 4

pages = 20

Answer: 20

6
The table shows a proportional relationship. Find the missing cookies.
batchescookies
218
436
6?
872
Show Answer

In a proportional relationship, every pair uses the same ratio.

cookies = 9 × batches

cookies = 9 × 6

cookies = 54

Answer: 54

7
The table shows a proportional relationship. Find the missing ounces.
poundsounces
1?
232
348
464
Show Answer

In a proportional relationship, every pair uses the same ratio.

ounces = 16 × pounds

ounces = 16 × 1

ounces = 16

Answer: 16

8
The table shows a proportional relationship. Find the missing cards.
packscards
48
816
1224
16?
Show Answer

In a proportional relationship, every pair uses the same ratio.

cards = 2 × packs

cards = 2 × 16

cards = 32

Answer: 32

9
The table shows a proportional relationship. Find the missing minutes.
songsminutes
13
26
3?
412
Show Answer

In a proportional relationship, every pair uses the same ratio.

minutes = 3 × songs

minutes = 3 × 3

minutes = 9

Answer: 9

10
The table shows a proportional relationship. Find the missing apples.
bagsapples
2?
416
624
832
Show Answer

In a proportional relationship, every pair uses the same ratio.

apples = 4 × bags

apples = 4 × 2

apples = 8

Answer: 8

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