Problem solving with graphing linear relationships | Maths

Starter quiz

The gradient is a measure of how __________ a line is.

steep ✓

high

low

long
Which of the values are missing from the table of values for the first five terms of the sequence $7n-10$ ?

$-10$

$-3$ ✓

$4$ ✓

$7$

$18$ ✓
A pupil is saving money. They start with $\pounds30$ and save $\pounds8$ per week. How much will they have after $5$ weeks?

'£70' ✓
At what coordinates do these two lines intersect?

$(0,5)$

$(2,0)$

$(5,15)$ ✓

$(15,5)$

$(1,3)$
Which of these lines has the steeper gradient?

A ✓

B

C
Will this table of values plot a linear relationship?

Yes. The $y$ values have a constant difference of $+5$ .

No. Both variables are not changing at a constant rate. ✓

It's impossible to tell until plotted.

On a time distance graph a greater speed is represented by a steeper ______.

'gradient' ✓
The graph shows the cost of two taxi companies for miles travelled. Which firm is cheapest for a $3$ mile journey?

A

B ✓

They cost the same price for that many miles.

It's impossible to tell from the graph.
The graph shows the cost of two taxi companies for miles travelled. At how many miles do they cost the same price?

'5' ✓
$The graph shows the cost of two taxi companies for miles travelled. How much do firm A charge per mile in <Math>\pounds</Math>?$

The graph shows the cost of two taxi companies for miles travelled. How much do firm A charge per mile in $\pounds$ ?

'1.50' ✓
This graph shows the time $(t)$ and distance $(d)$ of a car journey. For how long did the car stop?

$8$ minutes

$10$ minutes

$15$ minutes ✓

$25$ minutes

$30$ minutes
This graph shows the time $(t)$ and distance $(d)$ of a car journey. When is the car moving fastest?

$0$ to $10$ minutes

$10$ to $25$ minutes

$25$ to $30$ minutes ✓

$0$ to $8$ kilometres

$8$ to $16$ kilometres ✓

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Real life relationships can be represented using a linear graph.
Real life problems can be solved using a linear graph.
Switching between algebraic and graphical representations can help solve real life problems.

There is one answer to everything in maths.

We often see arithmetic and equations with one answer but, maths can be used to compare and justify multiple answers to a single problem.

Rate of change - The rate of change is how one variable changes with respect to another. If constant, there is a linear relationship.
Gradient - The gradient is a measure of how steep a line is.