To determine which equation correctly represents the relationship between the number of hours Samir works ([tex]\(y\)[/tex]) and the number of hours Mitul works ([tex]\(x\)[/tex]), let's break down the problem:
1. Identify Given Ratios:
- For every 19 hours that Mitul works, Samir works 15 hours.
2. Formulate the Relationship:
- We need to find [tex]\(y\)[/tex], the number of hours Samir works, in terms of [tex]\(x\)[/tex], the number of hours Mitul works.
3. Ratio Application:
- Since Samir works 15 hours for every 19 hours that Mitul works, we can set up the following proportion:
[tex]\[
\frac{y}{x} = \frac{15}{19}
\][/tex]
4. Solve for [tex]\(y\)[/tex]:
- To express [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex], we multiply both sides of the equation by [tex]\(x\)[/tex]:
[tex]\[
y = \frac{15}{19} x
\][/tex]
Therefore, the equation that correctly models the relationship between the hours that Samir works and the hours that Mitul works is:
[tex]\[ y = \frac{15}{19} x \][/tex]
So, the correct choice from the given options is:
[tex]\[ y = \frac{15}{19} x \][/tex]
