Worksheet comparing linear functions through tables, graphs, and equations.

To solve the problems in the worksheet, we need to analyze the given tables, graphs, and equations of linear functions. Let's go through each problem step by step.

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Problem 1:

Function A vs. Function B

#### Step 1: Analyze the Graphs
- Function A: The graph shows a line with a positive slope.
- Function B: The graph shows a line with a negative slope.

#### Step 2: Compare the Slopes
- The slope of Function A is positive because the line rises as we move from left to right.
- The slope of Function B is negative because the line falls as we move from left to right.

#### Answer:
Function A has a greater slope than Function B.

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Problem 2:

Function M vs. Function N

#### Step 1: Analyze the Equations
- Function M: \( y = 3x - 5 \)
- Function N: \( y = -2x + 3 \)

#### Step 2: Identify the Slopes
- The slope of Function M is \( 3 \) (from the coefficient of \( x \)).
- The slope of Function N is \( -2 \) (from the coefficient of \( x \)).

#### Step 3: Compare the Slopes
- The slope of Function M (\( 3 \)) is greater than the slope of Function N (\( -2 \)).

#### Answer:
Function M has a greater slope than Function N.

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Problem 3:

Function P vs. Function Q

#### Step 1: Analyze the Tables
- Function P:
\[
\begin{array}{c|c}
x & y \\
\hline
-4 & -8 \\
0 & 0 \\
2 & 4 \\
\end{array}
\]
- Function Q: \( y = 3x + 6 \)

#### Step 2: Calculate the Slope for Function P
- Use the formula for slope: \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
- Using points \((0, 0)\) and \((2, 4)\):
\[
m = \frac{4 - 0}{2 - 0} = \frac{4}{2} = 2
\]
- So, the slope of Function P is \( 2 \).

#### Step 3: Identify the Slope for Function Q
- From the equation \( y = 3x + 6 \), the slope is \( 3 \).

#### Step 4: Compare the Slopes
- The slope of Function P (\( 2 \)) is less than the slope of Function Q (\( 3 \)).

#### Answer:
Function Q has a greater slope than Function P.

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Problem 4:

Function R vs. Function S

#### Step 1: Analyze the Graphs
- Function R: The graph shows a steeper line.
- Function S: The graph shows a less steep line.

#### Step 2: Compare the Slopes
- The slope of Function R is steeper, indicating a larger absolute value of the slope.
- The slope of Function S is less steep, indicating a smaller absolute value of the slope.

#### Answer:
Function R has a greater slope than Function S.

---

Problem 5:

Function C vs. Function D

#### Step 1: Analyze the Tables
- Function C:
\[
\begin{array}{c|c}
x & y \\
\hline
-2 & -7 \\
0 & -3 \\
2 & -1 \\
\end{array}
\]
- Function D: \( y = -\frac{1}{2}x + 1 \)

#### Step 2: Identify the y-intercept for Function C
- The y-intercept is the value of \( y \) when \( x = 0 \).
- From the table, when \( x = 0 \), \( y = -3 \).
- So, the y-intercept of Function C is \( -3 \).

#### Step 3: Identify the y-intercept for Function D
- From the equation \( y = -\frac{1}{2}x + 1 \), the y-intercept is \( 1 \).

#### Step 4: Compare the y-intercepts
- The y-intercept of Function C (\( -3 \)) is less than the y-intercept of Function D (\( 1 \)).

#### Answer:
Function D has a greater y-intercept than Function C.

---

Problem 6:

Function E vs. Function F

#### Step 1: Analyze the Tables
- Function E:
\[
\begin{array}{c|c}
x & y \\
\hline
-1 & -5 \\
0 & 0 \\
1 & 5 \\
\end{array}
\]
- Function F: \( y = 6x + 2 \)

#### Step 2: Identify the Slope for Function E
- Use the formula for slope: \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
- Using points \((0, 0)\) and \((1, 5)\):
\[
m = \frac{5 - 0}{1 - 0} = \frac{5}{1} = 5
\]
- So, the slope of Function E is \( 5 \).

#### Step 3: Identify the Slope for Function F
- From the equation \( y = 6x + 2 \), the slope is \( 6 \).

#### Step 4: Compare the Slopes
- The slope of Function E (\( 5 \)) is less than the slope of Function F (\( 6 \)).

#### Answer:
Function F has a greater slope than Function E.

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Final Answers:

1. Function A has a greater slope than Function B.
2. Function M has a greater slope than Function N.
3. Function Q has a greater slope than Function P.
4. Function R has a greater slope than Function S.
5. Function D has a greater y-intercept than Function C.
6. Function F has a greater slope than Function E.

\[
\boxed{
\text{1. Function A, 2. Function M, 3. Function Q, 4. Function R, 5. Function D, 6. Function F}
}
\]