Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis; Jay Abramson; Sharon North; Amy Baldwin; Alyssa Howell

2.3.1 • Finding Connections between Graphs and Equations

Warm Up

Use the following information to answer questions 1 – 8. Here are graphs of two equations in a system.

Determine if each of these systems could be represented by the graphs. Be prepared to explain how you know.

1.

${\begin{matrix} x + 2 y = 8 \\ x = - 5 \end{matrix}$

No.

2.

How do you know if the system of equations in question 1 could be represented by the graph?

Compare your answer:

Your answer may vary, but here is a sample. No, it cannot be represented by the graph. The graph for $x = - 5$ would be on the left side of the vertical axis, which is not what is shown.

3.

${\begin{matrix} y = - 7 x + 13 \\ y = - 1 \end{matrix}$

No.

4.

How do you know if the system of equations in question 3 could be represented by the graph?

Compare your answer:

Your answer may vary, but here is a sample. No, it cannot be represented by the graph. The graph for $y = - 1$ would be a horizontal line, but no horizontal line is shown.

5.

${\begin{matrix} 3 x = 8 \\ 3 x + y = 15 \end{matrix}$

Yes.

6.

How do you know if the system of equations in question 5 could be represented by the graph?

Compare your answer:

Your answer may vary, but here is a sample. Yes. $3 x = 8$ can be rearranged into $x = \frac{8}{3}$ . The graph for $x = \frac{8}{3}$ is a vertical line to the right of the vertical axis. $3 x + y = 15$ can be rewritten as $y = - 3 x + 15$ . Its graph has a negative slope and a positive $y$ -value for the vertical intercept.

7.

${\begin{matrix} y = 2 x - 7 \\ 4 + y = 12 \end{matrix}$

No.

8.

ow do you know if the system of equations in question 7 could be represented by the graph?

Compare your answer:

Your answer may vary, but here is a sample. No. The graph for $y = 2 x - 7$ would have a positive slope and a negative $y$ -value for the vertical intercept, neither of which matches the given graphs.

2.3.1 Finding Connections between Graphs and Equations

Warm Up