When your parents were younger, having a mobile phone was a big deal—if they were lucky enough to have one! But owning the phone was only half the challenge. Choosing the right phone plan was the other tricky part.

Question

Back then, neither texting nor talking was unlimited. In fact, carriers charged for both!

Here’s an example: VoiceStream offered a plan for $40 per month, plus an additional charge of 5 cents for every text sent.
If y represents the total monthly cost and x represents the number of texts sent, what equation in slope-intercept form represents this plan?

Answer 1

To represent the VoiceStream plan in slope-intercept form, we need to establish the relationship between the total monthly cost \( y \) and the number of texts sent \( x \).

The plan has a fixed monthly cost of $40, and an additional charge of 5 cents (or $0.05) for every text sent.

The total cost can be expressed as:

• The fixed cost of $40.
• The variable cost, which is $0.05 multiplied by the number of texts sent \( x \).

Putting this together, the equation for the total monthly cost \( y \) can be written as:

\[ y = 0.05x + 40 \]

In this equation:

• The slope \( 0.05 \) represents the cost per text sent.
• The y-intercept \( 40 \) represents the fixed monthly cost.

So the equation in slope-intercept form is:

\[ y = 0.05x + 40 \]