Defining features of linear relationships | Maths | Quizalize & Oak National Academy

Starter quiz

Two variables that change together at a constant rate when plotted on a graph will form a ______ relationship.

'linear' ✓
Match the arithmetic sequences to the descriptors.

$11,4,-3,-10, ...$

⇔

Starts at $11$ and decreases by $7$ . ✓

$11,7,3,-1, ...$

⇔

Starts at $11$ and decreases by $4$ . ✓

$7,11,15,19, ...$

⇔

Starts at $7$ and increases by $4$ . ✓

$7,18,29,40, ...$

⇔

Starts at $7$ and increases by $11$ . ✓

$11,15,19,23, ...$

⇔

Starts at $11$ and increases by $4$ . ✓

$7,3,-1,-5, ...$

⇔

Starts at $7$ and decreases by $4$ . ✓
Match the common differences to the arithmetic sequences.

$-8,-3,2,7, ...$

⇔

$+5$ ✓

$7,2,-3,-8, ...$

⇔

$-5$ ✓

$-8,-6,-4,-2, ...$

⇔

$+2$ ✓

$-4,-6,-8,-10, ...$

⇔

$-2$ ✓

$4,1,-2,-5, ...$

⇔

$-3$ ✓

$-14,-11,-8,-5, ...$

⇔

$+3$ ✓
Which of the below coordinates can you see plotted here?

$(-2,-2)$ ✓

$(-2,2)$

$(-1,2)$ ✓

$(6,0)$

$(0,6)$ ✓
Here is an arithmetic (linear) sequence for which we are given the second and fourth terms. Which of the below are the missing terms?

$0.87$ ✓

$0.5$

$0.8$

$0.69$ ✓

$0.51$ ✓
For the linear relationship $y=15-7x$ what is the $y$ coordinate when the $x$ coordinate is $1.5$ ? State your answer as a decimal.

'4.5' ✓

The ______ is how quickly one variable changes with respect to another. If the change is constant, there is a linear relationship between the variables.

rate of change ✓

rate of increase

rate of decrease

increase

decrease
Here is a table of values for the relationship $y=2x-3$ . Which statements are true of the rate of change between the two variables?

For every change of $+1$ in $x$ there is a change of $-2$ in $y$ .

For every change of $+1$ in $x$ there is a change of $+2$ in $y$ . ✓

For every change of $+1$ in $y$ there is a change of $+2$ in $x$ .

For every change of $+2$ in $x$ there is a change of $+4$ in $y$ . ✓
What constant rate of change is shown by this linear graph?

For every change of $+1$ in $x$ there is a change of $+3$ in $y$ .

For every change of $+1$ in $y$ there is a change of $+3$ in $x$ .

For every change of $+1$ in $x$ there is a change of $-3$ in $y$ . ✓

For every change of $+1$ in $y$ there is a change of $-3$ in $x$ .
An ______ is the coordinate where a line or curve meets a given axis.

interval

inequality

intercept ✓

axis

$x$ coordinate
What is the $y$ -intercept of this line?

$2$

$(2,0)$

$-2$

$(0,4)$ ✓

$4$
Which unique statement describes this line?

Starts at $4$ and has a rate of change of $-2$

Starts at $2$ and has a rate of change of $+2$

$y$ -intercept at $(4,0)$ and has a rate of change of $+2$

$y$ -intercept at $(0,4)$ and has a rate of change of $-2$ ✓

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The arithmetic sequence 5n+2 starts at 7 so the linear equation y=5x+2 'starts' somewhere.

y=5x+2 has no start and no end; it goes on infinitely. However, all linear equations have a y-intercept and this helps define them.

Rate of change - The rate of change is how quickly one variable changes with respect to another. If constant, there is a linear relationship.
Intercept - An intercept is the coordinate where a line or curve meets a given axis.