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.