The correct equation that models Emma's situation is [tex]\(y = 20x + 0.15s\)[/tex].
Here's the detailed step-by-step breakdown:
1. Identify the Format of the Equation:
The equation is in the form [tex]\(y = mx + cs\)[/tex], where [tex]\(m\)[/tex] and [tex]\(c\)[/tex] are constants.
2. Compare Given Equations with the Desired Form:
- [tex]\( y = 20x + 0.15 \)[/tex]
- [tex]\( y = 20x + 15 \)[/tex]
- [tex]\( y = 20x + 0.15s \)[/tex]
- [tex]\( y = 20x + 15s \)[/tex]
3. Check for Presence of [tex]\(s\)[/tex]:
We are looking for an equation with [tex]\(s\)[/tex] included in it. Therefore, we can eliminate equations without [tex]\(s\)[/tex]:
- [tex]\( y = 20x + 0.15 \)[/tex] (no [tex]\(s\)[/tex], eliminate)
- [tex]\( y = 20x + 15 \)[/tex] (no [tex]\(s\)[/tex], eliminate)
4. Evaluate Equations with [tex]\(s\)[/tex]:
- [tex]\( y = 20x + 0.15s \)[/tex]
- [tex]\( y = 20x + 15s \)[/tex]
5. Choose the Correct Constant:
- The constant added to [tex]\(20x\)[/tex] should be [tex]\(0.15s\)[/tex], not [tex]\(15s\)[/tex].
6. Match with the Desired Form [tex]\(y = mx + cs\)[/tex]:
The equation [tex]\(y = 20x + 0.15s\)[/tex] fits the desired format [tex]\(y = mx + cs\)[/tex] perfectly with [tex]\(m = 20\)[/tex] and [tex]\(c = 0.15\)[/tex].
Therefore, the equation that correctly models Emma's situation is:
[tex]\[ y = 20x + 0.15s \][/tex]
