To find the correct equation that models the relationship between the number of hours Samir and Mitul work, let's analyze the given information step-by-step.
1. We know that for every 19 hours Mitul works, Samir works 15 hours.
2. Hence, the ratio of Samir's hours to Mitul's hours is [tex]\( \frac{15}{19} \)[/tex].
To model this relationship mathematically where:
- [tex]\( y \)[/tex] is the number of hours that Samir works.
- [tex]\( x \)[/tex] is the number of hours that Mitul works.
The ratio can be expressed as:
[tex]\[ \frac{y}{x} = \frac{15}{19} \][/tex]
To isolate [tex]\( y \)[/tex], we can multiply both sides of the equation by [tex]\( x \)[/tex]:
[tex]\[ y = \frac{15}{19} x \][/tex]
Thus, the correct equation that models the relationship between the number of hours that Samir and Mitul work is:
[tex]\[ y = \frac{15}{19} x \][/tex]
So, the correct option is:
[tex]\[ y = \frac{15}{19} x \][/tex]
