Features of linear relationships | Maths | Quizalize & Oak National Academy

Starter quiz

The sequence $7,13,19,25,31, ...$ is arithmetic (linear) because:
- is it increasing.
- the terms are all positive.
- it has a common, constant difference between terms. ✓
- the terms are all odd numbers.
Which of these sequences is arithmetic (linear)?
- $5,10,15,20,25, ...$ ✓
- $6,10,15,21,28, ...$
- $6,1,-4,-9,-14, ...$ ✓
- $2.1,2.4,2.7,3,3.3, ...$ ✓
- $1,2,4,8,16, ...$
Which of the below values will be a $y$ coordinate in this table of values for the relationship $y=4x+5$ ?
- $-5$
- $-3$ ✓
- $-1$
- $4$
- $5$ ✓
Here are the second and fifth terms of an arithmetic sequence. Which are the missing terms?
- $4$
- $6$ ✓
- $12$
- $14$ ✓
- $18$ ✓
What is the $10^{\text{th}}$ term of the sequence $2n^3$ ?
- $60$
- $200$
- $2000$ ✓
- $8000$
What will the $y$ coordinate be when $x=-2$ for the relationship $y=10-3x$ ?
- $-16$
- $-4$
- $4$
- $16$ ✓

The relationship between two variables is linear when they change together ______.
- with a constant multiplier
- at a constant rate ✓
- with the same difference
Does this table of values represent a linear relationship?
- No. The difference between $-2$ and $3$ in $y$ is different.
- No. $x$ changes by $+1$ whereas $y$ changes by $+5$ .
- Yes. The $y$ values change constantly by $+5$ as $x$ changes by $+1$ . ✓
- We can't know until we plot it and draw a line.
What is the constant rate of change in this relationship?
- $1$
- $2$
- $4$
- $+1$ in $x$ and $+2$ in $y$
- $+1$ in $x$ and $+4$ in $y$ ✓
Does this table of values represent a linear relationship?
- No. The $x$ values don't change by $1$ .
- No. The $y$ values are decreasing, not increasing.
- Yes. The $y$ values change by $-3$ for every change of $+2$ in $x$ . ✓
- We can't know until we plot it and draw a line.
Which of these rules will form a linear relationship?
- $y=6x-7$ ✓
- $y=7-6x$ ✓
- $y^3=7-x$
- $y=6x^2-7$
- $6y=7-x$ ✓
Match the coordinate to the linear relationship it fits.
- $(3,12)$
  
  ⇔
  
  $y=5x-3$ ✓
- $(3,-12)$
  
  ⇔
  
  $y=3-5x$ ✓
- $(6,-3)$
  
  ⇔
  
  $y = {1\over 3}x-5$ ✓
- $(6,10)$
  
  ⇔
  
  $y = {5x\over 3}$ ✓
- $(8,1)$
  
  ⇔
  
  $5y=x-3$ ✓

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A linear graph can be described by its features.
All the coordinates on the line fit the relationship.
The relationship between the coordinates can be described algebraically.
These linear relationships have particular features.
You can move between the algebraic statement and the graphical representation and back using coordinates.

Only equations in the form $y=mx+c$ are linear. All equations are linear.

There are many forms that linear equations can take, however they always share a common feature. The variables have exponents of $1$ .

Linear - The relationship between two variables is linear when they change together at a constant rate and form a straight line when plotted.