Applied exercises: Linear functions

Basic fee: 20€

Costs per minute: 0.35€

The monthly bill is given by taking the basic charge and adding the cost for the called minutes.

Monthly bill for 40 minutes

Mr. Smith was on the phone for 40 minutes.

Calculate the cost for these 40 minutes.

$40\cdot 0.35€=14€$

Add them to the basic fee.

Monthly costs = $20€+14€=34€$

Mr. Smith pays 34€ if he calls for 40 minutes.

Monthly bill for 80 minutes

Mr. Smith was on the phone for 80 minutes.

Calculate the cost for these 80 minutes.

$80\cdot 0.35€=28€$

Add them to the basic fee.

Monthly costs = $20€+28€=48€$

Mr. Smith pays 48€ if he calls for 80 minutes.

Monthly bill for 120 minutes

Mr. Smith was on the phone for 120 minutes.

Calculate the cost for these 120 minutes.

$120\cdot 0.35€=42€$

Add them to the basic fee.

Monthly costs = $20€+42€=62€$

Mr. Smith pays 62€ if he calls for 120 minutes.

Monthly cost = basic fee + cost of minutes called.

Let $x$ be the number of minutes called.

Use it to calculate the cost.

Costs = $20€+0.35€\cdot x$

Express this by a linear function.

$f(x)=0.35\cdot x+20$

$f(x)=0.35x+20$

This function has $y$-axis intercept 20, so it intersects the $y$-axis at $(0|20)$. Its slope is 0.35. So draw a point, e.g., at $(10|20+10\cdot 0.35)=(10|23.5)$. Connect these points by a line. This gives you the desired graph.