Drawing reciprocal graphs | Maths | Quizalize & Oak National Academy

Starter quiz

$1\over7$ is the __________ of $7$

divisor

factor

inverse

reciprocal ✓
What is the value of $y$ when $x=5$ in the equation $y=15x$ ? ______

'75' ✓
What is the value of $y$ when $x=5$ in the equation $y={15\over{x}}$ ? ______

'3' ✓
What is the value of $y$ when $x={1\over{2}}$ in the equation $y=6x$ ?

12

6

3 ✓

-3
What is the value of $y$ when $x={1\over{2}}$ in the equation $y={6\over{x}}$ ?

36

12 ✓

6

3

-3
What is the value of $y$ when $x=-{1\over{2}}$ in the equation $y={6\over{x}}$ ? A calculator might be useful to check your calculation here.

-12 ✓

-3

3

12

Exit quiz

__________ graphs can have the form $y={k\over{x}}$

Cubic

Linear

Quadratic

Reciprocal ✓
Which coordinate pairs will appear in the graph of $y={30\over{x}}$ ?

(1, 30) ✓

(30, 1) ✓

(2, 15) ✓

(3, 15)

(6, 10)
Which coordinate pairs will appear in the graph of $y={45\over{x}}$ ?

(-9, -5) ✓

(-9, 5)

(0, 45)

(-5, 9)

(-5, -9) ✓
Laura say this is not the graph of a reciprocal equation. How can you tell Laura is correct?

The $y$ values should be positive, not negative.

It does not intercept the $x$ or $y$ axis.

The curves should be in diagonally opposite quadrants. ✓

It is the graph of a reciprocal equation.
Which of these reciprocal graphs will intercept the $x$ axis?

$y={1\over{x}}$

$y=-{1\over{x}}$

$y={1\over{x}}+1$ ✓

$y={1\over{x}}-1$ ✓

$y={0.1\over{x}}$
Which coordinate pair is the $x$ intercept for the graph of $y={42\over{x}}-6$ ?

(7, 0) ✓

(6, 0)

(0, -6)

(-6, 0)

(-7, 0)

Worksheet

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Lesson Details

Key learning points

Inverse proportion graphs are reciprocal graphs.
A table of values can be useful to identify coordinate pairs which satisfy the equation.
By substituting the values for x, you can calculate corresponding values for y.
If used correctly, your calculator can be a powerful tool to speed up calculations.

Common misconception

$1 \\over 0$ evaluates to give $0$

Get pupils to consider what happens when $x=1\\over2$ , $x=1\\over3$ , $x=1\\over4$ etc. This will help them spot the role of the $y$ axis as asymptote for themselves.

Keywords

Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1