Choose whether each situation represents a direct variation or inverse variation.
(1 point)
Direct Variation Inverse Variation
The cost per fitness class at a gym that costs
$13 a month with unlimited classes included.
x/y=27
5y=x
It costs $30 per piano lesson
y/x=−42
The cost per fitness class at a gym that costs $13 a month with unlimited classes included represents a direct variation.
x/y=27 represents an inverse variation.
5y=x represents a direct variation.
It costs $30 per piano lesson represents a direct variation (not an inverse variation).
y/x=−42
y/x=−42 represents an inverse variation.
To determine whether each situation represents a direct variation or inverse variation, we need to compare the equations given.
1) The cost per fitness class at a gym that costs $13 a month with unlimited classes included:
To find the variation type, we can rewrite the equation x/y = 27 into y = kx form, where k is the constant of variation:
y = 27x
Since the equation is in the form y = kx, where k is a non-zero constant, this represents direct variation.
2) The equation given is 5y = x:
This equation is already in the form y = kx, where k is the constant of variation.
Since the equation is in the form y = kx, where k is a non-zero constant, this also represents direct variation.
3) It costs $30 per piano lesson:
To find the variation type, we can rewrite the equation y/x = -42 into y = k/x form, where k is the constant of variation:
y = -42/x
Since the equation is in the form y = k/x, where k is a non-zero constant, this represents inverse variation.
Therefore, the situations can be categorized as follows:
Direct Variation:
- The cost per fitness class at a gym that costs $13 a month with unlimited classes included.
- The equation 5y = x
Inverse Variation:
- It costs $30 per piano lesson.