What you’ll learn to do: Plot points on the rectangular coordinate system and find solutions to linear equations
Cyclists speed toward the finish line.Which cyclist will win the race? What will the winning time be? How many seconds will separate the winner from the runner-up? One way to summarize the information from the race is by creating a graph. In this chapter, we will discuss the basic concepts of graphing. The applications of graphing go far beyond races. They are used to present information in almost every field, including healthcare, business, and entertainment.
Before you get started in this module, try a few practice problems and review prior concepts.
Readiness Quiz
1)
If you missed this problem, review the example below.
Evaluate [latex]x+7[/latex] when
- [latex]x=3[/latex]
- [latex]x=12[/latex]
Show Solution
Solution:
1. To evaluate, substitute [latex]3[/latex] for [latex]x[/latex] in the expression, and then simplify.
|
[latex]x+7[/latex] |
| Substitute. |
[latex]\color{red}{3}+7[/latex] |
| Add. |
[latex]10[/latex] |
When [latex]x=3[/latex], the expression [latex]x+7[/latex] has a value of [latex]10[/latex].
2. To evaluate, substitute [latex]12[/latex] for [latex]x[/latex] in the expression, and then simplify.
|
[latex]x+7[/latex] |
| Substitute. |
[latex]\color{red}{12}+7[/latex] |
| Add. |
[latex]19[/latex] |
When [latex]x=12[/latex], the expression [latex]x+7[/latex] has a value of [latex]19[/latex].
Notice that we got different results for parts 1 and 2 even though we started with the same expression. This is because the values used for [latex]x[/latex] were different. When we evaluate an expression, the value varies depending on the value used for the variable.
2)
If you missed this problem, review this example.
[latex]\text{Evaluate }3x+4y - 6\text{ when }x=10\text{ and }y=2[/latex].
Show Solution
SolutionThis expression contains two variables, so we must make two substitutions.
|
[latex]3x+4y-6[/latex] |
| Substitute [latex]\color{red}{10}[/latex] for x and [latex]\color{blue}{2}[/latex] for y. |
[latex]3(\color{red}{10})+4(\color{blue}{2})-6[/latex] |
| Multiply. |
[latex]30+8-6[/latex] |
| Add and subtract left to right. |
[latex]32[/latex] |
When [latex]x=10[/latex] and [latex]y=2[/latex], the expression [latex]3x+4y - 6[/latex] has a value of [latex]32[/latex].
STOP!
You Have Now Completed This Section. Go Back To Your Course Menu And Complete The Practice Problems For This Section
3)
If you missed this problem, review the following video.
