M
Math Coach Amy
Amy Ferguson Moncure

7th Grade Math · Unit 5

Graph a Proportional
Relationship

Graph a straight line that passes through the origin.

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Key Ideas Easy Medium Hard
What to Remember

Through the origin

The graph of y = mx is a straight line through the origin.

A point and a slope

From a point and a slope, also plot (0, 0).

Level 1

Easy

Graph 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 = 5x
Show Answer

y = 5x

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

Another point is (1, 5).

The line continues in both directions through those points.

−112−1123456(0, 0)(1, 5)

Answer: through (0, 0) and (1, 5)

5
Graph the proportional relationship.
y = 6x
Show Answer

y = 6x

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

Another point is (1, 6).

The line continues in both directions through those points.

−112−11234567(0, 0)(1, 6)

Answer: through (0, 0) and (1, 6)

6
Graph the proportional relationship.
y = 7x
Show Answer

y = 7x

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

Another point is (1, 7).

The line continues in both directions through those points.

−112−112345678(0, 0)(1, 7)

Answer: through (0, 0) and (1, 7)

7
Graph the proportional relationship.
y = 8x
Show Answer

y = 8x

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

Another point is (1, 8).

The line continues in both directions through those points.

−112−1123456789(0, 0)(1, 8)

Answer: through (0, 0) and (1, 8)

8
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)

9
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)

10
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)

Level 2

Medium

A point on y = mx

Example
Graph the proportional relationship with this slope and point.
slope 2, point (3, 6)

m = 2 and the line contains (3, 6).

A proportional relationship also contains (0, 0).

y = 2x

−112−1123(0, 0)(1, 2)

Answer: y = 2x

1
Graph the proportional relationship with this slope and point.
slope 1, point (5, 5)
Show Answer

m = 1 and the line contains (5, 5).

A proportional relationship also contains (0, 0).

y = x

−112−112(0, 0)(1, 1)

Answer: y = x

2
Graph the proportional relationship with this slope and point.
slope 3, point (1, 3)
Show Answer

m = 3 and the line contains (1, 3).

A proportional relationship also contains (0, 0).

y = 3x

−112−11234(0, 0)(1, 3)

Answer: y = 3x

3
Graph the proportional relationship with this slope and point.
slope 4, point (2, 8)
Show Answer

m = 4 and the line contains (2, 8).

A proportional relationship also contains (0, 0).

y = 4x

−112−112345(0, 0)(1, 4)

Answer: y = 4x

4
Graph the proportional relationship with this slope and point.
slope 5, point (1, 5)
Show Answer

m = 5 and the line contains (1, 5).

A proportional relationship also contains (0, 0).

y = 5x

−112−1123456(0, 0)(1, 5)

Answer: y = 5x

5
Graph the proportional relationship with this slope and point.
slope 12, point (2, 1)
Show Answer

m = 12 and the line contains (2, 1).

A proportional relationship also contains (0, 0).

y = 12x

−1123−112(0, 0)(2, 1)

Answer: y = 12x

6
Graph the proportional relationship with this slope and point.
slope 12, point (6, 3)
Show Answer

m = 12 and the line contains (6, 3).

A proportional relationship also contains (0, 0).

y = 12x

−1123−112(0, 0)(2, 1)

Answer: y = 12x

7
Graph the proportional relationship with this slope and point.
slope 13, point (3, 1)
Show Answer

m = 13 and the line contains (3, 1).

A proportional relationship also contains (0, 0).

y = 13x

−11234−112(0, 0)(3, 1)

Answer: y = 13x

8
Graph the proportional relationship with this slope and point.
slope 14, point (4, 1)
Show Answer

m = 14 and the line contains (4, 1).

A proportional relationship also contains (0, 0).

y = 14x

−112345−112(0, 0)(4, 1)

Answer: y = 14x

9
Graph the proportional relationship with this slope and point.
slope 23, point (3, 2)
Show Answer

m = 23 and the line contains (3, 2).

A proportional relationship also contains (0, 0).

y = 23x

−11234−1123(0, 0)(3, 2)

Answer: y = 23x

10
Graph the proportional relationship with this slope and point.
slope 34, point (8, 6)
Show Answer

m = 34 and the line contains (8, 6).

A proportional relationship also contains (0, 0).

y = 34x

−112345−11234(0, 0)(4, 3)

Answer: y = 34x

Level 3

Hard

A negative slope

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.

−112−2−11(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.

−112−3−2−11(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.

−112−4−3−2−11(0, 0)(1, −3)

Answer: through (0, 0) and (1, −3)

3
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)

4
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)

5
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.

−112−5−4−3−2−11(0, 0)(1, −4)

Answer: through (0, 0) and (1, −4)

6
Graph the proportional relationship with this slope and point.
slope −1, point (3, −3)
Show Answer

m = −1 and the line contains (3, −3).

A proportional relationship also contains (0, 0).

y = −x

−112−2−11(0, 0)(1, −1)

Answer: y = −x

7
Graph the proportional relationship with this slope and point.
slope −2, point (2, −4)
Show Answer

m = −2 and the line contains (2, −4).

A proportional relationship also contains (0, 0).

y = −2x

−112−3−2−11(0, 0)(1, −2)

Answer: y = −2x

8
Graph the proportional relationship with this slope and point.
slope −3, point (1, −3)
Show Answer

m = −3 and the line contains (1, −3).

A proportional relationship also contains (0, 0).

y = −3x

−112−4−3−2−11(0, 0)(1, −3)

Answer: y = −3x

9
Graph the proportional relationship with this slope and point.
slope −12, point (4, −2)
Show Answer

m = −12 and the line contains (4, −2).

A proportional relationship also contains (0, 0).

y = −12x

−1123−2−11(0, 0)(2, −1)

Answer: y = −12x

10
Graph the proportional relationship with this slope and point.
slope −32, point (2, −3)
Show Answer

m = −32 and the line contains (2, −3).

A proportional relationship also contains (0, 0).

y = −32x

−1123−4−3−2−11(0, 0)(2, −3)

Answer: y = −32x

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