Checking and securing plotting a relationship | Maths

Starter quiz

In algebra, when we replace variables with values we call this ______.

transforming

substituting ✓

calculating

solving
What is this coordinate?

$(4,2)$

$(2,4)$ ✓

$2,4$

$4,2$
Which statements are true of this coordinate?

The $y$ -coordinate is double the $x$ -coordinate. ✓

The $y$ -coordinate is half the $x$ -coordinate.

The $y$ -coordinate is $2$ more than the $x$ -coordinate. ✓

The $y$ -coordinate is $2$ more than the $x$ -coordinate. ✓

The $x$ -coordinate and $y$ -coordinate sum to $4$ .
What is the value of the expression $5x-1$ when $x=3$ ?

'14' ✓
What is the value of the expression $5x-1$ when $x=-3$ ?

$-16$ ✓

$-14$

$14$

$16$
Starting with the lowest, order the value of these expressions when $x=2$ .

1

⇔

$4x-5$

2

⇔

$10-3x$

3

⇔

$7-x$

4

⇔

$3x$

5

⇔

$x+5$

All of these coordinates fit the relationship $x+y=5$ . This is an example of a ______ relationship.

quadratic

linear ✓

diagonal

constant
What is the relationship between the $x$ and $y$ coordinates for the set $(-1,-2)$ , $(0,0)$ , and $(1,2)$ ?

$x$ is always $1$ away from $y$ .

$x$ is always $1$ more than $y$ .

$x$ is double $y$ .

$y$ is double $x$ . ✓
If we plot these coordinates will we see a linear relationship? $(0,3)$ , $(1,4)$ , $(2,5)$ , $(3,7)$ , and $(4,7)$ .

Yes. This is an increasing linear relationship.

No. They do not fit the same rule. ✓

It's impossible to know until we plot them.
Match the coordinates to the respective rule.

$(1,5)$

⇔

$y=3x+2$ ✓

$(3,2)$

⇔

$x+y=5$ ✓

$(5,2)$

⇔

$y=x-3$ ✓

$(3,5)$

⇔

$y=2x-1$ ✓
These coordinates all fit the relationship $y=2x^2$ . Which words describe this relationship?

Linear

Non-linear ✓

Straight line

Curve ✓
Some pupils are sharing $36$ sweets. As the number of pupils ( $p$ ) varies, the numbers of sweets ( $s$ ) each student gets varies. Which of the below represents this relationship?

${p\over 36}=s$

${36\over p}=s$ ✓

${s\over 36}=p$

$p=36s$

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A relationship between two variables can be described using a rule.
This relationship can be used to generate coordinate pairs.
These pairs can be plotted on a graph.
The shape of the curve made will give information about the relationship between the points.
All the points on the curve satisfy the relationship.

All graphs are linear and if graphs are not linear you join points with straight line segments.

Explore $n+2, 2n$ and $x^2$ . \"I see $n$ and 2; they must be similar\" pupils think. Get them to compare numerically, then graphically.

Substitute - Substitute means to put in place of another. In Algebra, substitution can be used to replace variables with values.