GCSE Maths · Higher · Chapter 10: Linear graphs · Lesson 3

Real-life graphs and graphical solutions

Grades 4–7About 40 minutesNo calculator29 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
Find the gradient of the line through $(- 1, 1)$ and $(3, 9)$ .
[1 mark]
Answer
A2
Last lesson
Find the equation of the line through $(1, 2)$ and $(2, 1)$ .
[1 mark]
Answer
A3
From chapter 2
Write the multiplier for a decrease of $7%$ .
[1 mark]
Answer
A4
From chapter 6
Find the sum of the interior angles of an 11-sided polygon.
[1 mark]
Answer

Grades 4–6

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

Example 1

A straight-line graph changes gallons into litres. It passes through $(0, 0)$ and $(10, 45)$ . Use it to change 18 gallons into litres.

Hint Work out how many litres one gallon is.

B1
A straight-line graph changes inches into centimetres. It passes through $(0, 0)$ and $(20, 50)$ . Change 14 inches into cm, and 85 cm into inches.
[2 marks]
Answer $\dots\dots$ cm and $\dots\dots$ inches

Example 2

The lines $y = 3 x - 4$ and $y = 11 - 2 x$ are drawn on a grid. Work out where they cross.

Hint Where they cross, both

y

values are the same.

B2
The lines $y = 4 x + 1$ and $y = 2 x + 9$ are drawn on a grid. Work out where they cross.
[3 marks]
Answer $(\dots\dots, \dots\dots)$

Grades 5–6

C1
A mechanic charges a fixed fee of £48 plus £21 for each hour. Write a formula for the charge $C$ pounds for $h$ hours, and use it for a 4-hour job.
[2 marks]
Answer $C = \dots\dots$ £ $\dots\dots$
C2
The graph of the cost of hiring a boat, £ $C$ , against the time, $h$ hours, is a straight line through $(0, 15)$ and $(4, 47)$ . What does the 15 mean, and what is the cost per hour?
[2 marks]

C3
Two lines cross at $(- 2, 5)$ . One of them is $y = 3 x + 11$ . The other has gradient $- 1$ . Work out the equation of the other line.
[2 marks]
Answer
C4
Do the lines $y = 3 x + 2$ and $y = 3 x - 5$ cross? Give a reason.
[1 mark]

Grades 6–7

D1
Ellie says, "The lines $y = 2 x + 1$ and $y = 13 - x$ cross at $(3, 7)$ , because $2 \times 3 + 1 = 7$ ."
Explain why Ellie is wrong, and find where the lines do cross.
[3 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 read a conversion graph and say what a gradient means in a real context.
I can write a cost formula and use it to compare two options.
I can solve two equations together by finding where their lines cross.

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