Which equation(s) represents a proportional relationship?
A) y=7x²
B) y=2+3x
C) y=1/2x
D) y=5-x
B, C, D
Which equation(s) represents a proportional relationship?
A) 5+x
B) y=4x
C) 7x²
D) 2-x
A, B, D
Remember that a proportional relationship between x and y means that y = kx. There can be no extra constants floating around.
A is a proportional relationship between y and x^2
Only C is a p.r between y and x.
For #2, same thing applies.
To determine if an equation represents a proportional relationship, we need to look for a specific pattern. In a proportional relationship, the ratio between the dependent variable (y) and the independent variable (x) remains constant.
For the first question, let's analyze each equation:
A) y = 7x²: This equation is not proportional because as x increases, y increases exponentially due to the square term.
B) y = 2 + 3x: This equation is proportional because the constant term (2) does not affect the ratio between y and x. The ratio between y and x remains constant at 3:1.
C) y = 1/2x: This equation is proportional because the ratio between y and x is always constant at 1:2.
D) y = 5 - x: This equation is proportional because as x increases, y decreases at a constant rate.
Therefore, the equations B, C, and D represent proportional relationships.
For the second question, let's analyze each equation:
A) 5 + x: This equation is not proportional because the ratio between y and x changes depending on the value of x.
B) y = 4x: This equation is proportional because the ratio between y and x is always constant at 4:1.
C) 7x²: This equation is not proportional because as x increases, the value of y increases exponentially due to the squared term.
D) 2 - x: This equation is not proportional because the ratio between y and x changes depending on the value of x.
Therefore, the equations A, B, and D represent proportional relationships.