Question

proportional vs. non - proportional
put your answers in alphabetical order!

1. which of the following linear equations are proportional? circle all that apply.

a. ( y = 3x + 2 )
b. ( y=\frac{1}{2}x )
c. ( y = 0.75x )
d. ( y=\frac{3}{4}x - 8 )
e. ( y = 7x + 5 )

1. which of the following linear equations are non - proportional? circle all that apply.

a. ( y = 4x + 8 )
b. ( y=\frac{1}{3}x - 6 )
c. ( y = 0.4x )
d. ( y=-\frac{3}{2}x )
e. ( y=-x - 5 )

Explanation:

Step1: Recall the form of proportional equations

A proportional linear equation has the form \(y = kx\) (where \(k\) is a non - zero constant, and the \(y\) - intercept \(b = 0\)).

Step2: Analyze equations for question 11

• For \(y = 3x+2\), \(b = 2

eq0\), so it is non - proportional.

• For \(y=\frac{1}{2}x\), it is in the form \(y = kx\) (\(k=\frac{1}{2}\)), so it is proportional.
• For \(y = 0.75x\), it is in the form \(y = kx\) (\(k = 0.75\)), so it is proportional.
• For \(y=\frac{3}{4}x - 8\), \(b=-8

eq0\), so it is non - proportional.

• For \(y = 7x+5\), \(b = 5

eq0\), so it is non - proportional.

Step3: Analyze equations for question 12

• For \(y = 4x+8\), \(b = 8

eq0\), so it is non - proportional.

• For \(y=\frac{1}{3}x-6\), \(b=-6

eq0\), so it is non - proportional.

• For \(y = 0.4x\), it is in the form \(y = kx\) (\(k = 0.4\)), so it is proportional (not for question 12).
• For \(y=-\frac{3}{2}x\), it is in the form \(y = kx\) (\(k=-\frac{3}{2}\)), so it is proportional (not for question 12).
• For \(y=-x - 5\), \(b=-5

eq0\), so it is non - proportional.

Since we need to put answers in alphabetical order:
For question 11 (proportional), after checking the forms, \(b:y=\frac{1}{2}x\) and \(c:y = 0.75x\) are proportional.
For question 12 (non - proportional), \(a:y = 4x+8\), \(b:y=\frac{1}{3}x - 6\), \(e:y=-x - 5\) are non - proportional.

Answer:

1. b, c
2. a, b, e