GCSE Maths · Higher · Chapter 10: Linear graphs · Lesson 1

Drawing linear graphs and gradient

Grades 4–7About 50 minutesNo calculator36 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Work out $3 x^{2} + 6$ when $x = - 4$ .
[1 mark]
Answer
A2
From chapter 8
Make $r$ the subject of $A = 2 r^{2}$ .
[1 mark]
Answer
A3
Last lesson
A pyramid has a square base of side 7 cm and height 12 cm. Find its volume.
[1 mark]
Answer
A4
Key Stage 3
Work out $\frac{3}{7}$ of $56$ .
[1 mark]
Answer

Grades 4–6

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

Example 1

Work out the gradient of the line through $(1, 9)$ and $(4, - 3)$ .

Hint Change in

y

divided by change in

x

B1
Work out the gradient of the line through $(- 3, - 4)$ and $(1, 6)$ .
[2 marks]
Answer

Example 2

The line $5 x + 2 y = 20$ crosses the $x$ -axis at $A$ and the $y$ -axis at $B$ . Find $A$ and $B$ , then work out the gradient of the line.

Hint On the

x

-axis

y = 0

; on the

y

-axis

x = 0

B2
The line $2 x + 3 y = 18$ crosses the $x$ -axis at $A$ and the $y$ -axis at $B$ . Find $A$ and $B$ , then work out the gradient of the line.
[3 marks]
Answer $A (\dots, \dots)$ $B (\dots, \dots)$ gradient $\dots\dots$

Grades 5–6

C1
Which two of these lines are parallel? $A$ : $y = 3 x - 7$ $B$ : $2 y = 6 x - 5$ $C$ : $y = 1 - 3 x$ $D$ : $3 y = x + 6$ . Give a reason.
[2 marks]
Answer $\dots$ and $\dots$
C2
Write down the gradient and the $y$ -intercept of the line $4 y = 6 x + 12$ .
[2 marks]
Answergradient $\dots\dots$ $y$ -intercept $\dots\dots$

C3
A line has gradient $- 2$ and crosses the $y$ -axis at $(0, 7)$ . Write down its equation, and find where it crosses the $x$ -axis.
[2 marks]
Answer $y = \dots\dots$ $(\dots\dots, \dots\dots)$
C4
Does the point $(6, 13)$ lie on the line $y = 3 x - 4$ ? Show how you decide.
[2 marks]
C5
The diagram shows a straight line. Work out its gradient and write down its $y$ -intercept.
[2 marks]
Answergradient $\dots\dots$ $y$ -intercept $\dots\dots$
C6
The points $A (- 1, - 4)$ , $B (3, 8)$ and $C (5, k)$ lie on one straight line. Work out the value of $k$ .
[2 marks]
Answer

Grades 6–7

D1
Mia says, "The line through $(2, 1)$ and $(6, 9)$ goes 4 across and 8 up, so its gradient is $\frac{1}{2}$ ."
Explain why Mia is wrong, and give the correct gradient.
[2 marks]

Grade 8 and beyond

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

Colour one circle on each line.

	Not yet	Nearly	Yes
I can draw a straight line from a table of values, and work out a gradient from two points or from a graph.
I can read the gradient and $y$ -intercept from an equation, and write $y = m x + c$ .
I can find where a line crosses the axes by the cover-up method.

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