KS3 Maths · Year 7 · Chapter 7: Graphs · Lesson 2

Gradient (steepness) of a straight line

Year 7About 70 minutesNo calculator46 marks

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Date

Do Now

Quick questions to start.

A1
Needed today
Work out $\frac{11 - 3}{6 - 2}$ .
[1 mark]
Answer
A2
Needed today
For the line $y = 4 x - 7$ , work out $y$ when $x = 0$ .
[1 mark]
Answer
A3
Last lesson
Where does the line $y = 2 x - 8$ cross the $x$ -axis?
[1 mark]
Answer
A4
From chapter 4
Increase $80$ kg by $15%$ .
[1 mark]
Answer

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

Work out the gradient of the line.

Hint Pick two points on the line where it crosses the grid exactly. Gradient

=

\div

across.

B1
Work out the gradient of the line.
[2 marks]
Answer

Example 2

Write down the gradient and the $y$ -intercept of $y = 6 x - 1$ and of $y = 4 - 3 x$ .

Hint In

y = m x + c

the gradient is the number multiplying

x

, sign and all.

c

is where the line cuts the

y

-axis.

B2
Write down the gradient and the $y$ -intercept of $y = 2 x - 9$ and of $y = 8 - 5 x$ .
[2 marks]
Answer

Example 3

Find the equation of the line.

Hint Read

c

where the line cuts the

y

-axis. For the gradient, a line going down to the right has a negative gradient.

B3
Find the equation of the line.
[3 marks]
Answer

Example 4

A line passes through $(0, 6)$ and $(2, 14)$ . Find its equation.

Hint

(0, 6)

is on the

y

-axis, so it gives

c

. Then the gradient is up

\div

across between the two points.

B4
A line passes through $(0, - 5)$ and $(3, 1)$ . Find its equation.
[2 marks]
Answer

Practice

Year 7

C1
Work out the gradient of line $P$ and the gradient of line $Q$ .
[4 marks]
Answer
C2
Write down the equation of the line with (i) gradient $- 3$ that crosses the $y$ -axis at $(0, 8)$ , (ii) gradient $\frac{1}{2}$ that crosses the $y$ -axis at $(0, - 6)$ .
[2 marks]
Answer

C3
Which two of these lines are parallel? Give a reason. $y = 4 x + 5 y = x + 4 y = 5 - 4 x y = 4 x - 9$
[2 marks]
Answer
C4
Write $2 y = 8 x + 6$ in the form $y = m x + c$ . Then write down its gradient.
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
Ben says, "The line $y = 7 - 2 x$ has gradient $7$ ."
Ben is wrong. Explain why, and write down the gradient and the $y$ -intercept of the line.
[3 marks]
Answer

D2
The line $L$ is drawn on the grid.
(a)
Work out the gradient of $L$ .
[2 marks]
Answer
(b)
Write down the equation of $L$ .
[1 mark]
Answer
(c)
Line $M$ is parallel to $L$ and passes through $(0, 6)$ . Write down the equation of $M$ .
[1 mark]
Answer
Total for D2: 4 marks
D3
A straight line passes through the points $(1, 7)$ and $(4, 16)$ .
(a)
Work out the gradient of the line.
[2 marks]
Answer
(b)
Find the equation of the line.
[2 marks]
Answer
(c)
Does the point $(10, 35)$ lie on the line? Show how you know.
[1 mark]
Answer
Total for D3: 5 marks
D4
Here are sketches of three lines. Match each sketch to its equation. $y = 2 x - 1 y = 2 x + 4 y = 3 - x$
[3 marks]
Answer
D5
A line passes through $(0, 8)$ and $(3, 2)$ . Find the equation of the line, and the point where it crosses the $x$ -axis.
[4 marks]
Answer $y = \dots\dots$ and $(\dots\dots, \dots\dots)$

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
Line $P$ has gradient $2$ and passes through $(3, 11)$ . Line $Q$ is parallel to $y = 5 - x$ and passes through $(0, 11)$ . Find the point where $P$ and $Q$ cross.
[4 marks]
Hint 1 · What to try
Find the equation of each line in the form $y = m x + c$ .
Hint 2 · The first line
$P$ : $11 = 2 \times 3 + c$ , so $y = 2 x + 5$ . $Q$ has gradient $- 1$ , so $y = 11 - x$ .
Hint 3 · The full method
Where they cross, $2 x + 5 = 11 - x$ , so $3 x = 6$ .
Answer $(\dots\dots, \dots\dots)$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can work out the gradient of a line from a graph.
I can read the gradient and the $y$ -intercept from $y = m x + c$ .
I can find the equation of a line from a graph or from two points.
I know that parallel lines have the same gradient.

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