Reading from graphs | Maths | Quizalize & Oak National Academy

Starter quiz

The relationship between two ______ is linear if, when plotted on a pair of axes, a straight line is formed.

'variables' ✓
What is the minimum number of coordinates needed to plot the graph of $y=5x+3$ ?

1

2 ✓

3

4

5
Andeep plots the graph of the linear equation $4x + 6y = 24$ . When $y=0$ then $y=$ ______.

'6' ✓
Laura is plotting the graph of the line $3y + 5x=15$ . She only wants to plot two points. Which of these points would be the best points for Laura to use?

When $x=0$ ✓

When $x=1$

When $x=2$

When $x=3$ ✓

When $x=4$
Match each pair of coordinates with the equation of the line that coordinates are on.

$(3, 0)$

⇔

$y=2x-6$ ✓

$(3, 1)$

⇔

$3y=x$ ✓

$(3, 2)$

⇔

$x+y=5$ ✓

$(3, 3)$

⇔

$y=x$ ✓

$(3, 4)$

⇔

$2y-3x=-1$ ✓
Jun wants to draw the graph of $y = 0.2x + 2.2$ for positive values of $x$ . The coordinates of the first point on the line that has positive integer coordinates are ______.

'(4, 3)' ✓

Exit quiz

The graph of a ______ equation is called a parabola.

'quadratic' ✓
Use the graph of $y =3x-4$ to solve the equation $3x-4=8$ . The solution is $x=$ ______.

'4' ✓
$Use the graph of <Math>y =7.4 x+12.95</Math> to estimate the value of <Math>7.4\times 3+12.95</Math>.$

Use the graph of $y =7.4 x+12.95$ to estimate the value of $7.4\times 3+12.95$ .

25

30

35 ✓

40

45
How many solutions are there to the equation $x^2+2=10$ . Use the graph of $y=x^2+2$ to help you.

0

1

2 ✓

3

Infinite
$Use the graph of <Math>y=\frac{1}{2} x^2+1</Math> to help you solve the equation <Math>\frac{1}{2}x^2+1=3</Math>.$

Use the graph of $y=\frac{1}{2} x^2+1$ to help you solve the equation $\frac{1}{2}x^2+1=3$ .

$x=-2$ ✓

$x=-1$

$x=1$

$x=2$ ✓

$x=3$
This parabola models the flight of a cricket ball being thrown. The cricket ball is above a height of 5 metres for a distance of ______ metres altogether.

'16' ✓

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Lesson Details

Key learning points

If you have one value, you can use a linear graph to find its pair.
The pair of values will satisfy the linear equation.
If the x and y variables have context, then their values can be interpreted within that context.
With quadratic graphs, there may be more than one value to find.

Common misconception

Since linear equations (typically) have one solution, all equations have one solution.

Ask pupils to compare the graphical solution to a linear equation with the graphical solution to a quadratic equation. This will enable them to see that it is possible for a quadratic equation to have more than one solution.

Keywords

Linear - The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.
Quadratic - A quadratic is a an equation, graph, or sequence whereby the highest exponent of the variable is 2.
Parabola - A parabola is a curve where any point on the curve is an equal distance from a fixed point (the focus) and a fixed straight line (the directrix).