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Gradient and Intercept of a Line y = mx + c (2)

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

'Gradient and Intercept of a Line y = mx + c (2)' worksheet

Key stage:  KS 4

Curriculum topic:  Algebra

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

Difficulty level:  

down

Worksheet Overview

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 - 1 = x
2

 

Answer

 

y - 1 = x
2

 

Multiply both sides by 2 to get

y - 1 = 2x

 

Rearrange the equation to make y the subject by adding 1 to both sides.

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 - 3 = x
2

 

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

 

y - 4 = x
3

 

(3, 0)

(0, 3)

(4, 0)

(0, 4)

State the gradient of the line with equation:

 

y = 3 - 4x

State the gradient of the line with equation:

 

y - 4 = x
2

 

State the gradient of the line with equation:

 

y = -7

0

x

7

-7

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

 

y + 6 = x
3

 

 

(-6, 3)

(0, -6)

(-6, 0)

(0, 3)

State the gradient of the line with equation:

 

3 - y
= x
2

 

State the gradient of the line with equation:

 

y = 4 - 0.3x

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

  

1 - y
= x
4

 

(4, -1)

(0, 1)

(4, 0)

(0, -4)

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

 

y + 1
= x
-2

 

(0, 2)

(0, -1)

(0, 1)

(2, -1)

  • Question 1

State the gradient of the line with equation:

 

y - 3 = x
2

 

CORRECT ANSWER
2
  • Question 2

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

 

y - 4 = x
3

 

CORRECT ANSWER
(0, 4)
  • Question 3

State the gradient of the line with equation:

 

y = 3 - 4x

CORRECT ANSWER
-4
  • Question 4

State the gradient of the line with equation:

 

y - 4 = x
2

 

CORRECT ANSWER
2
  • Question 5

State the gradient of the line with equation:

 

y = -7

CORRECT ANSWER
0
EDDIE SAYS
This is y = 0x - 7
  • Question 6

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

 

y + 6 = x
3

 

 

CORRECT ANSWER
(0, -6)
  • Question 7

State the gradient of the line with equation:

 

3 - y
= x
2

 

CORRECT ANSWER
-2
  • Question 8

State the gradient of the line with equation:

 

y = 4 - 0.3x

CORRECT ANSWER
-0.3
  • Question 9

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

  

1 - y
= x
4

 

CORRECT ANSWER
(0, 1)
  • Question 10

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

 

y + 1
= x
-2

 

CORRECT ANSWER
(0, -1)
---- OR ----

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