KS3 Maths · Year 7 · Chapter 7: Graphs · Lesson 1

Graphs from linear equations

Year 7About 70 minutesNo calculator46 marks

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Date

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Quick questions to start.

A1
Needed today
Work out the value of $2 x - 3$ when $x = - 2$ .
[1 mark]
Answer
A2
Needed today
Solve $3 y + 2 = 14$ .
[1 mark]
Answer
A3
Last lesson
A prism has a cross-section of area $18$ cm² and a length of $7$ cm. Work out its volume.
[1 mark]
Answer
A4
From chapter 2
The point $(2, - 1)$ is moved $3$ units left and $4$ units up. Write down its new coordinates.
[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

Complete the table for $y = 2 x + 5$ . Then draw the graph.

Hint Double each

x

first, then add

5

B1
Complete the table for $y = 3 x - 1$ .
[2 marks]

Example 2

Do the points $(4, 9)$ and $(- 1, - 5)$ lie on the line $y = 3 x - 2$ ?

Hint Put the

x

of the point into the equation and see if you get its

y

B2
Which of the points $(2, 1)$ , $(- 3, 11)$ and $(5, - 8)$ lie on the line $y = 5 - 2 x$ ?
[2 marks]
Answer

Example 3

Find where the line $2 y + x = 6$ crosses each axis, and the point on it where $x = 2$ . Draw the line.

Hint On the

y

-axis

x = 0

. On the

x

-axis

y = 0

B3
Find where the line $4 y + 3 x = 12$ crosses each axis, and the point on it where $x = 8$ .
[3 marks]
Answer

Example 4

The grid shows $y = x + 3$ , $y = x + 1$ and $y = x - 2$ . What is the same about the three lines? Where will $y = x + 5$ cross the $y$ -axis?

Hint Look at the number after the

x

, and where each line meets the

y

-axis.

B4
Which of these lines are parallel to $y = 2 x + 1$ ? Write down where each of those crosses the $y$ -axis. $y = 2 x - 4 y = x + 1 y = 2 x + 6$
[2 marks]
Answer

Practice

Year 7

C1
Complete the table for $y = 7 - x$ .
[2 marks]
C2
Draw the line $x + 3 y = 6$ on the grid. Use the points where it crosses the axes.
[3 marks]

C3
These lines are $y = x$ , $y = 3 x$ , $y = \frac{1}{2} x$ and $y = 5 x$ . (i) Which point do all four pass through? (ii) Which line is the steepest? (iii) Which line passes through $(6, 3)$ ?
[3 marks]
Answer
C4
Where does the line $y = 3 x - 6$ cross (i) the $y$ -axis, (ii) the $x$ -axis?
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
Amira says that the line $2 y + 5 x = 10$ crosses the $x$ -axis at the point $(5, 0)$ .
Amira is wrong. Explain her mistake, and write down where the line does cross the $x$ -axis.
[3 marks]
Answer $(\dots\dots, \dots\dots)$

D2
The points $(k, 13)$ and $(- 2, m)$ lie on the line $y = 4 x - 3$ .
(a)
Work out the value of $k$ .
[2 marks]
Answer
(b)
Work out the value of $m$ .
[1 mark]
Answer
Total for D2: 3 marks
D3
Three lines $A$ , $B$ and $C$ are drawn on the grid. Match each line to its equation. $y = x + 2 y = 4 - x y = 2 x - 1$
[3 marks]
Answer
D4
This question is about the line $y = 4 - 2 x$ .
(a)
Complete the table of values.
[2 marks]
(b)
On the grid, draw the graph of $y = 4 - 2 x$ for values of $x$ from $- 1$ to $3$ .
[2 marks]
(c)
Use your graph to find the value of $x$ when $y = - 1$ .
[1 mark]
Answer
Total for D4: 5 marks
D5
On the grid, draw the lines $y = x + 1$ and $y = 7 - 2 x$ . Write down the coordinates of the point where they cross.
[5 marks]
Answer $(\dots\dots, \dots\dots)$

Extension

Stretch

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

E1
The line $a y + 2 x = 18$ passes through the point $(3, 4)$ . Work out the value of $a$ . Then find where the line crosses the $y$ -axis.
[4 marks]
Hint 1 · What to try
The point $(3, 4)$ is on the line, so $x = 3$ and $y = 4$ make the equation true.
Hint 2 · The first line
$4 a + 6 = 18$ , so $4 a = 12$ .
Hint 3 · The full method
$a = 3$ . On the $y$ -axis $x = 0$ , so $3 y = 18$ .
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can complete a table of values and draw a straight-line graph.
I can draw a line from the points where it crosses the axes.
I can test whether a point lies on a line.
I can tell from their equations which lines are parallel.

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