To determine which equation in the form [tex]\( y = mx + cs \)[/tex] models Emma's situation, let's carefully examine each of the given options:
1. [tex]\( y = 20x + 0.15 \)[/tex]
2. [tex]\( y = 20x + 15 \)[/tex]
3. [tex]\( y = 20x + 0.15s \)[/tex]
4. [tex]\( y = 20x + 15s \)[/tex]
The form [tex]\( y = mx + cs \)[/tex] specifies that the equation must have:
- A term [tex]\( mx \)[/tex] where [tex]\( m \)[/tex] is a constant coefficient of [tex]\( x \)[/tex]
- A term [tex]\( cs \)[/tex] where [tex]\( c \)[/tex] is a constant coefficient, and [tex]\( s \)[/tex] is another variable.
Now, let's evaluate each option:
- Option 1: [tex]\( y = 20x + 0.15 \)[/tex]
- This does contain a term [tex]\( 20x \)[/tex] but lacks a term involving [tex]\( s \)[/tex], i.e., there is no [tex]\( cs \)[/tex] term.
- Option 2: [tex]\( y = 20x + 15 \)[/tex]
- This again contains a term [tex]\( 20x \)[/tex] but no term involving [tex]\( s \)[/tex].
- Option 3: [tex]\( y = 20x + 0.15s \)[/tex]
- This includes [tex]\( 20x \)[/tex] as the [tex]\( mx \)[/tex] term and [tex]\( 0.15s \)[/tex] as the [tex]\( cs \)[/tex] term. This fits the given form perfectly.
- Option 4: [tex]\( y = 20x + 15s \)[/tex]
- This also includes [tex]\( 20x \)[/tex] as the [tex]\( mx \)[/tex] term and [tex]\( 15s \)[/tex] as the [tex]\( cs \)[/tex] term, which also fits the given form.
Since both Option 3 and Option 4 fit the form [tex]\( y = mx + cs \)[/tex], we need to choose the most appropriate one. Given typical scenarios, the coefficient [tex]\( c \)[/tex] is often a smaller decimal value instead of a larger whole number. Hence, the most suitable option is:
[tex]\[ y = 20x + 0.15s \][/tex]
Therefore, the correct equation modeling Emma's situation is represented by Option 3:
[tex]\[ y = 20x + 0.15s \][/tex]
