What is the gradient of y = 5x + 2?

5. m is the number multiplying x.

What is the equation of the line with gradient 2 and y-intercept 3?

y = 2x + 3. y = mx + c with m = 2 and c = 3.

What is the gradient of the line 2y = 8x + 6?

4. Divide through by 2: y = 4x + 3.

A line has gradient 1 and passes through (0, 5). What is its equation?

y = x + 5. c is 5, since it crosses the y-axis there.

Equations of straight lines · Cambridge IGCSE Mathematics

In plain words

Every straight line has an equation of the form y = mx + c, and the two numbers tell you everything about it: m is how steep it is, and c is where it crosses the y-axis.

Three things to know

In y = mx + c, m is the gradient and c is the y-intercept.
To find the equation of a line: find the gradient, then put in the coordinates of a point on the line to find c.
If the equation isn't in the form y = …, rearrange it first. 2y = 6x + 4 is really y = 3x + 2.

Worked example

Find the equation of the line with gradient 3 that passes through (2, 5).

The equation is y = 3x + c.
Put in x = 2, y = 5: 5 = 6 + c, so c = −1.
y = 3x − 1.

Tips and tricks

Get the equation into the form y = mx + c before reading off the gradient.
Through two points: find the gradient first, then use either point to find c.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Equations of straight lines: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What is the gradient of y = 5x + 2?
- 2
- 5 (the answer)
- 7
- 5x
m is the number multiplying x.
Where does y = 3x − 4 cross the y-axis?
- at 3
- at 4
- at −4 (the answer)
- at 0
c is the y-intercept.
What is the equation of the line with gradient 2 and y-intercept 3?
- y = 3x + 2
- y = 2x + 3 (the answer)
- y = 2x − 3
- x = 2y + 3
y = mx + c with m = 2 and c = 3.
What is the gradient of the line 2y = 8x + 6?
- 8
- 6
- 4 (the answer)
- 3
Divide through by 2: y = 4x + 3.
A line has gradient 1 and passes through (0, 5). What is its equation?
- y = 5x
- y = 5x + 1
- y = x + 5 (the answer)
- y = x − 5
c is 5, since it crosses the y-axis there.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

3 questions, 7 marks. Write your answers on paper, then check them.

Equations of straight lines

Cambridge IGCSE Mathematics 0580 · 7 marks · papermunch.org

Name ______________________________ Date ______________

State the gradient and the y-intercept of y = 4x − 7.[2]
Show answerHide answer
Gradient 4, y-intercept −7.
I got this one
Find the equation of the line through (1, 1) and (3, 5).[3]
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y = 2x − 1. Gradient = 4 ÷ 2 = 2; 1 = 2 + c.
I got this one
Find the gradient of the line 2y = 6x + 4.[2]
Show answerHide answer
3. y = 3x + 2.
I got this one

Answers: Equations of straight lines

1. Gradient 4, y-intercept −7.
2. y = 2x − 1. Gradient = 4 ÷ 2 = 2; 1 = 2 + c.
3. 3. y = 3x + 2.