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Math Coach Amy
Amy Ferguson Moncure

7th Grade Math · Unit 5

Slope and
y = mx

Find the slope between two points and write y = mx.

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Key Ideas Easy Medium Hard
What to Remember

Through the origin

These two points include (0, 0), so the line is y = mx.

The slope is the change in y divided by the change in x.

A positive rate

A real life rate in this unit is a positive slope.

y = mx is direct variation through the origin.

Level 1

Easy

A positive whole-number slope

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

m = change in ychange in x

m = 11

m = 11

m = 1

y = x

Answer: y = x

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

m = change in ychange in x

m = 21

m = 21

m = 2

y = 2x

Answer: y = 2x

2
Find the slope, then write y = mx.
The points are (0, 0) and (1, 3).
Show Answer

m = change in ychange in x

m = 31

m = 31

m = 3

y = 3x

Answer: y = 3x

3
Find the slope, then write y = mx.
The points are (0, 0) and (1, 4).
Show Answer

m = change in ychange in x

m = 41

m = 41

m = 4

y = 4x

Answer: y = 4x

4
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

5
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

6
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

7
Find the slope, then write y = mx.
The points are (0, 0) and (3, 3).
Show Answer

m = change in ychange in x

m = 33

m = 33

m = 1

y = x

Answer: y = x

8
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

9
Find the slope, then write y = mx.
The points are (0, 0) and (4, 8).
Show Answer

m = change in ychange in x

m = 84

m = 84

m = 2

y = 2x

Answer: y = 2x

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

m = change in ychange in x

m = 55

m = 55

m = 1

y = x

Answer: y = x

Level 2

Medium

A positive fraction slope

Example
Find the slope, then write y = mx.
The points are (0, 0) and (4, 2).

m = change in ychange in x

m = 24

m = 24

m = 12

y = 12x

Answer: y = 12x

1
Find the slope, then write y = mx.
The points are (0, 0) and (6, 2).
Show Answer

m = change in ychange in x

m = 26

m = 26

m = 13

y = 13x

Answer: y = 13x

2
Find the slope, then write y = mx.
The points are (0, 0) and (6, 4).
Show Answer

m = change in ychange in x

m = 46

m = 46

m = 23

y = 23x

Answer: y = 23x

3
Find the slope, then write y = mx.
The points are (0, 0) and (8, 2).
Show Answer

m = change in ychange in x

m = 28

m = 28

m = 14

y = 14x

Answer: y = 14x

4
Find the slope, then write y = mx.
The points are (0, 0) and (8, 6).
Show Answer

m = change in ychange in x

m = 68

m = 68

m = 34

y = 34x

Answer: y = 34x

5
Find the slope, then write y = mx.
The points are (0, 0) and (10, 4).
Show Answer

m = change in ychange in x

m = 410

m = 410

m = 25

y = 25x

Answer: y = 25x

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

m = change in ychange in x

m = 610

m = 610

m = 35

y = 35x

Answer: y = 35x

7
Find the slope, then write y = mx.
The points are (0, 0) and (6, 9).
Show Answer

m = change in ychange in x

m = 96

m = 96

m = 32

y = 32x

Answer: y = 32x

8
Find the slope, then write y = mx.
The points are (0, 0) and (8, 12).
Show Answer

m = change in ychange in x

m = 128

m = 128

m = 32

y = 32x

Answer: y = 32x

9
Find the slope, then write y = mx.
The points are (0, 0) and (8, 10).
Show Answer

m = change in ychange in x

m = 108

m = 108

m = 54

y = 54x

Answer: y = 54x

10
Find the slope, then write y = mx.
The points are (0, 0) and (6, 8).
Show Answer

m = change in ychange in x

m = 86

m = 86

m = 43

y = 43x

Answer: y = 43x

Level 3

Hard

A negative slope

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

m = change in ychange in x

m = −11

m = −11

m = −1

y = −x

Answer: y = −x

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

m = change in ychange in x

m = −21

m = −21

m = −2

y = −2x

Answer: y = −2x

2
Find the slope, then write y = mx.
The points are (0, 0) and (1, −3).
Show Answer

m = change in ychange in x

m = −31

m = −31

m = −3

y = −3x

Answer: y = −3x

3
Find the slope, then write y = mx.
The points are (0, 0) and (1, −4).
Show Answer

m = change in ychange in x

m = −41

m = −41

m = −4

y = −4x

Answer: y = −4x

4
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

5
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

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

m = change in ychange in x

m = −33

m = −33

m = −1

y = −x

Answer: y = −x

7
Find the slope, then write y = mx.
The points are (0, 0) and (4, −2).
Show Answer

m = change in ychange in x

m = −24

m = −24

m = −12

y = −12x

Answer: y = −12x

8
Find the slope, then write y = mx.
The points are (0, 0) and (4, −6).
Show Answer

m = change in ychange in x

m = −64

m = −64

m = −32

y = −32x

Answer: y = −32x

9
Find the slope, then write y = mx.
The points are (0, 0) and (6, −4).
Show Answer

m = change in ychange in x

m = −46

m = −46

m = −23

y = −23x

Answer: y = −23x

10
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

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