Level 7 - NCEA Level 2

Finding Linear Equations in Context

Lesson

Now that we know how

we can put this to use to solve a range of real life applications.

It's all the same mathematics, but this time you will have a context to apply it to.

Some examples will be the best way to show you how the mathematics we have learnt can be applied to everyday situations.

A $carpenter$ charges a callout fee of $\$150$$150 plus $\$45$$45 per hour.

Write an equation to represent the total amount charged, $y$y, by the $carpenter$ as a function of the number of hours worked, $x$x.
What is the gradient of the function?
What does this gradient represent?
The total amount charged increases by $\$45$$45 for each additional hour of work.
A
The minimum amount charged by the $carpenter$ .
B
The total amount charged increases by $\$1$$1 for each additional $45$45 hours of work.
C
The total amount charged for $0$0 hours of work.
D
What is the value of the $y$y-intercept?
What does this $y$y-intercept represent?

Select all that apply.
The total amount charged increases by $\$150$$150 for each additional hour of work.
A
The maximum amount charged by the $carpenter$ .
B
The callout fee.
C
The minimum amount charged by the $carpenter$ .
D
Find the total amount charged by the $carpenter$ for $6$6 hours of work.

The table shows the linear relationship between the length of a mobile phone call and the cost of the call.

Length of call (minutes)	$1$1	$2$2	$3$3
Cost ( $dollars$ )	$7.6$7.6	$14.4$14.4	$21.2$21.2

Write an equation to represent the cost of a call, $y$y, as a function of the length of the call, $x$x.
What is the slope of the function?
What does the slope tell you?
The connection fee
A
The cost of each additional minute
B
The cost of the phone
C
The cost of a $1$1-minute call
D
What is the $y$y-intercept?
What does this $y$y-intercept tell you?
The cost of each additional minute
A
The cost of the phone
B
The cost of a $1$1-minute call
C
The connection fee
D
Find the cost of a $6$6-minute call.

The graph shows the amount of water remaining in a bucket that was initially full before a hole was made in its side.

Loading Graph...

What is the gradient of the function?
What is the $y$y-value of the $y$y-intercept?
Write an equation to represent the amount of water remaining in the bucket, $y$y, as a function of time, $x$x.
What does the slope tell you?
The amount of water remaining in the bucket after $2$2 minutes.
A
The amount of water that is flowing out of the hole every minute.
B
The time it takes for the bucket to be completely empty.
C
The time it takes the amount of water remaining in the bucket to drop by one litre.
D
What does the $y$y-intercept tell you?
The capacity of the bucket.
A
The amount of water remaining in the bucket after $30$30 minutes.
B
The amount of water remaining in the bucket when it is empty.
C
The size of the hole.
D
Find the amount of water remaining in the bucket after $54$54 minutes.