x : y = 1 : 5. Which is the correct equation? Why? a) y=5x b) y=x/5 c) y=x-4 d) y=x+4
a) y=5x is the correct equation.
This is because x:y = 1:5 means that for every 1 unit increase in x, y increases by 5 units. This can be expressed as y = 5x, where the value of x is multiplied by 5 to get the corresponding value of y.
Options b), c), and d) are not correct because they do not follow the given ratio of x:y = 1:5. Option b) shows the inverse ratio of y:x = 5:1, while options c) and d) show unrelated linear equations that do not correspond to the given ratio.
To determine the correct equation, we need to understand the relationship stated in the problem.
The expression "x : y = 1 : 5" means that for every 1 unit of x, there are 5 units of y.
Using this information, let's evaluate each equation:
a) y = 5x
In this equation, for every unit of x, there is 5 units of y, which aligns with the given relationship. Therefore, it is the correct equation.
b) y = x/5
In this equation, for every unit of x, there is only 1/5 of a unit of y. This does not match the given relationship, so it is not the correct equation.
c) y = x - 4
In this equation, the relationship between x and y does not match the given x : y = 1 : 5 since there is a subtraction involved. Therefore, it is not the correct equation.
d) y = x + 4
Similar to the previous equation, this equation does not align with the given relationship because of the addition involved. Hence, it is not the correct equation.
From the options provided, the correct equation is a) y = 5x, as it represents the correct ratio of 1 : 5 between x and y.