 # Straight Lines, Gradients and Linear Equations: y = mx + c

In this worksheet, students state the gradient of a straight line given its equation (y = mx + c). Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Use Linear Equations (Two Variables) and Gradients

Difficulty level:   ### QUESTION 1 of 10

The gradient of a line can easily be stated by looking carefully at its equation.

For the line with equation y = mx + c, the gradient is m.

m is the coefficient of x when in the form y = ......

Example

State the gradient of the line with equation y = 2x + 1

Comparing y = 2x + 1 to y = mx + c, we see that m = 2

The gradient of the line, m, is 2.

Check

The line is shown below.

y = 2x + 1 Note

The equation y = 2x + 1 can be rewritten in several ways as shown below.

They all represent the SAME line.

y = 1 + 2x

y - 1 = 2x

x = ½ (y - 1)

State the gradient of the line with equation:

y = 2x + 3

State the gradient of the line with equation:

y = 4x + 3

State the gradient of the line with equation:

y = 6x - 3

State the gradient of the line with equation:

y = 5x

State the gradient of the line with equation:

y = 5

State the gradient of the line with equation:

y = -6x + 3

State the gradient of the line with equation:

y = x + 3

State the gradient of the line with equation:

y = 4 + 3x

State the gradient of the line with equation:

y = 4 - 7x

State the gradient of the line with equation:

y + 3 = 2x

• Question 1

State the gradient of the line with equation:

y = 2x + 3

2
EDDIE SAYS

y = 2x + 3

m = 2

• Question 2

State the gradient of the line with equation:

y = 4x + 3

4
EDDIE SAYS

y = 4x + 3

m = 4

• Question 3

State the gradient of the line with equation:

y = 6x - 3

6
EDDIE SAYS

y = 6x - 3

m = 6

• Question 4

State the gradient of the line with equation:

y = 5x

5
EDDIE SAYS

y = 5x + 0

m = 5

• Question 5

State the gradient of the line with equation:

y = 5

0
EDDIE SAYS

y =0x + 5

m = 0

• Question 6

State the gradient of the line with equation:

y = -6x + 3

-6
EDDIE SAYS

y = -6x + 3

m = -6

• Question 7

State the gradient of the line with equation:

y = x + 3

1
EDDIE SAYS

y = 1x + 3

m = 1

• Question 8

State the gradient of the line with equation:

y = 4 + 3x

3
EDDIE SAYS

y = 3x + 4

m = 3

• Question 9

State the gradient of the line with equation:

y = 4 - 7x

-7
EDDIE SAYS

y = -7x + 4

m = -7

• Question 10

State the gradient of the line with equation:

y + 3 = 2x

2
EDDIE SAYS

y = 2x -3

m = 2

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