In the equation 3x+2y=9, if x increases by 2 then y does what?

Question

Increases by 2

Decreases by 6

Increases by 3

Increases by 6

Decreases by 3

 

Answer 1

Another way to get the answer is to put the equation in slope-intercept form: y = mx + b

 

3x+2y=9

 

2y = -3x + 9

 

y = (-3/2)x + 9/2

 

The slope (-3/2) tells you how much y changes for each unit change in x.

 

If x increases 2 units, y changes by mx = (-3/2) * 2

y changes by -3

 

Y decreases by 3.

 

Answer 2

"Increased by" are key words for addition.

3(x + 2) + 2(y + a) = 9

3x + 6 + 2y + 2a = 9

to keep equation the same "2a" should be opposite to 6

2a = - 6
a = - 3
3(x + 2) + 2(y - 3) = 9

"y" decreases by 3

Answer 3

3x + 2y = 9

y = (9 - 3x) / 2

 

if x increased by x'

y = (9 - 3(x+x') ) / 2

y = (9 - 3x - 3x') / 2

 

y changes by -3x'/2

 

if x' = +2,  y changes by -(3)(+2)/2 = -3

if x' = -6, y changes by  -(3)(-6)/2 = +9

if x' = +3, y changes by  -(3)(+3)/2 = -9/2 = -4.5

if x' = +6, y changes by  -(3)(+6)/2 = -9

if x' = -3, y changes by  -(3)(-3)/2 = +9/2 = +4.5

Answer 4

First, since 3x+2y=9, whenever x increases, y MUST decrease in order for the whole sum to stay the same. So you can eliminate three answers just by simple logic.

If x increases by 2, then 3 times x increases by 2 times three, that is by 6. Now if 3x increases by 6, then 2y MUST decrease by 6 in order for the sum 3x+2y to still be 9. If 2y decreases by 6, then each of the two y's must decrease by 3.

 

So, your answer is 'Decrease by 3', the last one.

Answer 5

I think that the easiest way to solve this problem is to plug in numbers and find the pattern.

 

First, I started by finding two numbers that make the equation true. I started with x=2, y=1.5. When I plug this into the equation, I get 6+3=9, which works.

 

Now, I need to increase x by 2, so x=4. Now, I get 12+2y=9, so y= -1.5.  y has changed from 1.5 to -1.5, so it has decreased by 3.

 

Next, I'll plug in a couple more numbers to see if this pattern holds true. If x=1, then y=3. 3+6=9. If I increase x to 3, then y must be 0; 9+0=9; y still decreases by 3.

 

I'll try one more number to make sure, this time a negative. If x=-1, then y=6. -3+12=9. So if I increase x to 1, y must equal 3. 3+6=9. y still decreases by 3.

 

The answer is that y decreases by 3

 

I would use this same method to solve the other questions in this set, but I would only plug in one or two numbers because I know this method works.

 

For example, if x=1, then y=3. If x decreases by 6, then it would equal -5, and y would have to equal 12. -15+24=9. y has gone from 3 to 12, which means it has increased by 9.

 

I hope that at this point, can solve the rest of the set on your own!