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Finite Mathematics and Applied Calculus

Stefan Waner, Steven R. Costenoble

Chapter 1: Chapter 1

Problem 1

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In Exercises $1-6,$ a table of values for a linear function is given. Fill in the missing value and calculate $m$ in each case. $$ \begin{array}{|c|c|c|c|} \hline x & -1 & 0 & 1 \\ \hline y & 5 & 8 & \\\ \hline \end{array} $$

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The missing y-value is 11, and the slope (m) of the linear function is 3.

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TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Identify Known Points

We are given the points (-1, 5) and (0, 8) from the table.

Step 2: Calculate the Slope Between the Known Points

Using the slope formula: $m = \frac{y2 - y1}{x2 - x1}$, we can calculate the slope between the known points (-1, 5) and (0, 8). $m = \frac{8-5}{0-(-1)} = \frac{3}{1} = 3$

Step 3: Use the Constant Slope to Find the Missing Value

Since the slope for a linear function is constant, we can use the fact that the slope between (-1, 5) and (1, y) should also be 3. Using the slope formula between (-1, 5) and (1, y): $3 = \frac{y-5}{1-(-1)}$

Step 4: Solve for the Missing Value

Now we can solve the equation to find the missing y-value: $3 = \frac{y-5}{2}$ Multiplying both sides by 2: $6 = y - 5$ Adding 5 to both sides: $11 = y$

Step 5: Fill in the Missing Value and State the Slope

Now we can fill in the missing value in the table and state the slope: $$ \begin{array}{|c|c|c|c|} \hline x & -1 & 0 & 1 \\\ \hline y & 5 & 8 & 11\\\ \hline \end{array} $$ The slope (m) of the linear function is 3.

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Chapter 1: Chapter 1

In Exercises \(1-6,\) a table of values for a linear function is given. Fill in the missing value and calculate \(m\) in each case. $$ \begin{array}{|c|c|c|c|} \hline x & -1 & 0 & 1 \\ \hline y & 5 & 8 & \\\ \hline \end{array} $$

Short Answer

Step by step solution

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Step 1: Identify Known Points

Step 2: Calculate the Slope Between the Known Points

Step 3: Use the Constant Slope to Find the Missing Value

Step 4: Solve for the Missing Value

Step 5: Fill in the Missing Value and State the Slope

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More chapters from the book ‘Finite Mathematics and Applied Calculus’

Chapter 0

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

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