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Chapter 7: Problem 88

For each situation, do the following. (a) Write an equation in the form \(y=m x+b\). (b) Find and interpret the ordered pair associated with the equation for \(x=5\). (c) Answer the question posed in the problem. Resident tuition at North Shore Community College is \(\$ 206\) per credit hour. There is also a \(\$ 300\) program fee for physical therapy. Let \(x\) represent the number of credit hours and \(y\) represent the cost in dollars. How much does it cost for a student in physical therapy to take 15 credit hours?

Short Answer

Expert verified
The cost for 15 credit hours is \$3390. The ordered pair for \(x=5\) is \((5, 1330)\).

Step by step solution

01

- Define the variables

Let the number of credit hours be represented by \(x\) and the cost in dollars be represented by \(y\). Given that the cost per credit hour is \$206 and there is an additional \$300 program fee, we need to establish the linear equation that links \(x\) and \(y\).
02

- Formulate the equation

In a linear equation of the form \(y = mx + b\), \(m\) represents the cost per credit hour and \(b\) represents the fixed program fee. From the given information, \(m=206\) and \(b=300\). Thus, the equation is \(y = 206x + 300\).
03

- Calculate the cost for 15 credit hours

Substitute \(x=15\) into the equation \(y = 206x + 300\): \[ y = 206(15) + 300 \] \[ y = 3090 + 300 \] \[ y = 3390 \] Therefore, the cost for 15 credit hours is \$3390.
04

- Find and interpret the ordered pair for \(x=5\)

To find the ordered pair for \(x=5\), substitute \(x=5\) into the equation \(y = 206x + 300\): \[ y = 206(5) + 300 \] \[ y = 1030 + 300 \] \[ y = 1330 \] The ordered pair is \((5, 1330)\), meaning that for 5 credit hours, the total cost is \$1330.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Slope-Intercept Form
In algebra, one of the most common forms to represent a linear equation is the slope-intercept form. It is written as \( y = mx + b \). Here, \( y \) represents the dependent variable, and \( x \) represents the independent variable. The term \( m \) is the slope, which shows how steep the line is and how much \( y \) changes for a given change in \( x \). The term \( b \) is the y-intercept, where the line crosses the y-axis.
In our example, the linear equation for calculating tuition is \( y = 206x + 300 \). Here, \( m = 206 \) because each credit hour costs \(206. The program fee is \)300, so \( b = 300 \).
This form clearly shows how the total cost depends on the number of credit hours.
Tuition Calculation
Calculating tuition can be straightforward using a linear equation. In this specific context, the main elements you need to know are:
  • Cost per credit hour: North Shore Community College charges \(206 per credit hour for residents.
  • Fixed program fee: There is an additional fixed fee of \)300 for the physical therapy program.

To calculate the total tuition (\

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