Match linear equations, tables, and graphs in this educational card activity.

To solve this task, we need to match each equation with its corresponding table or graph. Let's go through each equation and find the matching table or graph step by step.

Step 1: Analyze the Equations and Tables/Graphs

#### Equation 1: \( y = 2x + 1 \)
- Table Check: We need a table where \( y = 2x + 1 \).
- For \( x = 0 \), \( y = 2(0) + 1 = 1 \) (not in the table)
- For \( x = 1 \), \( y = 2(1) + 1 = 3 \) (not in the table)
- For \( x = 2 \), \( y = 2(2) + 1 = 5 \) (not in the table)
- For \( x = 3 \), \( y = 2(3) + 1 = 7 \) (not in the table)
- Graph Check: The graph should show a line with a positive slope of 2 and a y-intercept of 1.
- The graph with a positive slope and y-intercept of 1 is the one that matches.

#### Equation 2: \( y = -2x - 4 \)
- Table Check: We need a table where \( y = -2x - 4 \).
- For \( x = -1 \), \( y = -2(-1) - 4 = -2 \) (not in the table)
- For \( x = 0 \), \( y = -2(0) - 4 = -4 \) (in the table)
- For \( x = 1 \), \( y = -2(1) - 4 = -6 \) (not in the table)
- For \( x = 2 \), \( y = -2(2) - 4 = -8 \) (not in the table)
- Graph Check: The graph should show a line with a negative slope of -2 and a y-intercept of -4.
- The graph with a negative slope and y-intercept of -4 is the one that matches.

#### Equation 3: \( y = -3x + 4 \)
- Table Check: We need a table where \( y = -3x + 4 \).
- For \( x = 0 \), \( y = -3(0) + 4 = 4 \) (in the table)
- For \( x = 1 \), \( y = -3(1) + 4 = 1 \) (in the table)
- For \( x = 2 \), \( y = -3(2) + 4 = -2 \) (not in the table)
- For \( x = 3 \), \( y = -3(3) + 4 = -5 \) (not in the table)
- Graph Check: The graph should show a line with a negative slope of -3 and a y-intercept of 4.
- The graph with a negative slope and y-intercept of 4 is the one that matches.

#### Equation 4: \( y = -x - 1 \)
- Table Check: We need a table where \( y = -x - 1 \).
- For \( x = 0 \), \( y = -0 - 1 = -1 \) (not in the table)
- For \( x = 1 \), \( y = -1 - 1 = -2 \) (not in the table)
- For \( x = 2 \), \( y = -2 - 1 = -3 \) (not in the table)
- For \( x = 3 \), \( y = -3 - 1 = -4 \) (in the table)
- Graph Check: The graph should show a line with a negative slope of -1 and a y-intercept of -1.
- The graph with a negative slope and y-intercept of -1 is the one that matches.

#### Equation 5: \( y = x + 1 \)
- Table Check: We need a table where \( y = x + 1 \).
- For \( x = 0 \), \( y = 0 + 1 = 1 \) (not in the table)
- For \( x = 1 \), \( y = 1 + 1 = 2 \) (not in the table)
- For \( x = 2 \), \( y = 2 + 1 = 3 \) (not in the table)
- For \( x = 3 \), \( y = 3 + 1 = 4 \) (in the table)
- Graph Check: The graph should show a line with a positive slope of 1 and a y-intercept of 1.
- The graph with a positive slope and y-intercept of 1 is the one that matches.

#### Equation 6: \( y = 10x + 3 \)
- Table Check: We need a table where \( y = 10x + 3 \).
- For \( x = 0 \), \( y = 10(0) + 3 = 3 \) (in the table)
- For \( x = 1 \), \( y = 10(1) + 3 = 13 \) (not in the table)
- For \( x = 2 \), \( y = 10(2) + 3 = 23 \) (not in the table)
- For \( x = 3 \), \( y = 10(3) + 3 = 33 \) (not in the table)
- Graph Check: The graph should show a line with a positive slope of 10 and a y-intercept of 3.
- The graph with a positive slope and y-intercept of 3 is the one that matches.

#### Equation 7: \( y = 5x + 5 \)
- Table Check: We need a table where \( y = 5x + 5 \).
- For \( x = 0 \), \( y = 5(0) + 5 = 5 \) (in the table)
- For \( x = 1 \), \( y = 5(1) + 5 = 10 \) (not in the table)
- For \( x = 2 \), \( y = 5(2) + 5 = 15 \) (not in the table)
- For \( x = 3 \), \( y = 5(3) + 5 = 20 \) (not in the table)
- Graph Check: The graph should show a line with a positive slope of 5 and a y-intercept of 5.
- The graph with a positive slope and y-intercept of 5 is the one that matches.

Step 2: Match the Equations with the Tables/Graphs

- \( y = 2x + 1 \) matches the graph with a positive slope of 2 and y-intercept of 1.
- \( y = -2x - 4 \) matches the graph with a negative slope of -2 and y-intercept of -4.
- \( y = -3x + 4 \) matches the graph with a negative slope of -3 and y-intercept of 4.
- \( y = -x - 1 \) matches the graph with a negative slope of -1 and y-intercept of -1.
- \( y = x + 1 \) matches the graph with a positive slope of 1 and y-intercept of 1.
- \( y = 10x + 3 \) matches the graph with a positive slope of 10 and y-intercept of 3.
- \( y = 5x + 5 \) matches the graph with a positive slope of 5 and y-intercept of 5.

Final Answer

The correct matches are:
- \( y = 2x + 1 \) with the graph showing a positive slope of 2 and y-intercept of 1.
- \( y = -2x - 4 \) with the graph showing a negative slope of -2 and y-intercept of -4.
- \( y = -3x + 4 \) with the graph showing a negative slope of -3 and y-intercept of 4.
- \( y = -x - 1 \) with the graph showing a negative slope of -1 and y-intercept of -1.
- \( y = x + 1 \) with the graph showing a positive slope of 1 and y-intercept of 1.
- \( y = 10x + 3 \) with the graph showing a positive slope of 10 and y-intercept of 3.
- \( y = 5x + 5 \) with the graph showing a positive slope of 5 and y-intercept of 5.

Final Answer:
- \( y = 2x + 1 \) with the graph showing a positive slope of 2 and y-intercept of 1.
- \( y = -2x - 4 \) with the graph showing a negative slope of -2 and y-intercept of -4.
- \( y = -3x + 4 \) with the graph showing a negative slope of -3 and y-intercept of 4.
- \( y = -x - 1 \) with the graph showing a negative slope of -1 and y-intercept of -1.
- \( y = x + 1 \) with the graph showing a positive slope of 1 and y-intercept of 1.
- \( y = 10x + 3 \) with the graph showing a positive slope of 10 and y-intercept of 3.
- \( y = 5x + 5 \) with the graph showing a positive slope of 5 and y-intercept of 5.