# Gradient and Intercept of a Line y = mx + c (1)

In this worksheet, students state the gradient and intercept of a straight line given its equation.

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Use y = mx + c to Identify Parallel and Perpendicular Lines

Difficulty level:

### QUESTION 1 of 10

The gradient and intercept 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 and the intercept on

the y-axis is c.

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

c is the number on its own

Example

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

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

The gradient of the line, m, is 2 and the intercept, c, is 1, which means that it crosses the y-axis at (0, 1)

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 intercept on the y-axis of the line with equation:

y = 4x + 3

(3, 0)

(0, 3)

(4, 0)

(0, 4)

State the gradient of the line with equation:

y = 3 - 6x

State the gradient of the line with equation:

y = 5x

State the gradient of the line with equation:

y = 5

State the intercept on the y-axis of the line with equation:

y = -6x + 3

(-6, 3)

(0, -6)

(-6, 0)

(0, 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 intercept on the y-axis of the line with equation:

y = 4 - 7x

(4, -7)

(0, 4)

(4, 0)

(0, -7)

State the intercept on the y-axis of the line with equation:

y + 3 = 2x

(0, 3)

(0, -3)

(0, 2)

(2, -3)

• Question 1

State the gradient of the line with equation:

y = -2x + 3

-2
• Question 2

State the intercept on the y-axis of the line with equation:

y = 4x + 3

(0, 3)
• Question 3

State the gradient of the line with equation:

y = 3 - 6x

-6
• Question 4

State the gradient of the line with equation:

y = 5x

5
• Question 5

State the gradient of the line with equation:

y = 5

0
EDDIE SAYS
This is y = 0x + 5
• Question 6

State the intercept on the y-axis of the line with equation:

y = -6x + 3

(0, 3)
• Question 7

State the gradient of the line with equation:

y = x + 3

1
• Question 8

State the gradient of the line with equation:

y = 4 + 3x

3
• Question 9

State the intercept on the y-axis of the line with equation:

y = 4 - 7x

(0, 4)
• Question 10

State the intercept on the y-axis of the line with equation:

y + 3 = 2x