Algebra Slope Solving for Y Equation

[tathagata7]

Hello,

I'm trying to solve the below question on my SSAT prep:


Which equation represents a line parallel to the graph of 4x + 6y = 24 on the coordinate grid?

Answer:

My work:


4x + 6y = 24
-4x -4x

6y = -4x + 24

divide by 6 both sides

y = -4x/6 + 24/6

y = -2x/3 + 4

Don't know how they came up with the +8 in their answer ???

Thanks for your assistance.

 

[Ishuda]

Hello,

I'm trying to solve the below question on my SSAT prep:


Which equation represents a line parallel to the graph of 4x + 6y = 24 on the coordinate grid?

Answer:

My work:


4x + 6y = 24
-4x -4x

6y = -4x + 24

divide by 6 both sides

y = -4x/6 + 24/6

y = -2x/3 + 4

Don't know how they came up with the +8 in their answer ???

Thanks for your assistance.

What you want to look at for a question like this [parallel lines] is the coefficient of x (when the coefficient of y is 1), i.e. if
y = s x + b
we want to compare s's. It doesn't make any difference what b is, it just helps determine the distance between the two lines. So, the fact that the answer has a b of -8/3 doesn't matter, both the answer and your rearrangement of the equation for the original line have an s of -2/3 and so the lines are parallel.

 

[Steven G]

Hello,

I'm trying to solve the below question on my SSAT prep:


Which equation represents a line parallel to the graph of 4x + 6y = 24 on the coordinate grid?

Answer:

My work:


4x + 6y = 24
-4x -4x

6y = -4x + 24

divide by 6 both sides

y = -4x/6 + 24/6

y = -2x/3 + 4

Don't know how they came up with the +8 in their answer ??? They randomly picked 8

Thanks for your assistance.

Why did you write the original equation of the line as y = -2x/3 + 4? The answer to that question is so you can find (read off) the slope of the ORIGINAL line. The equation y = -2x/3 + 4 is the exact same equation as 4x + 6y = 24. Recall that two lines are parallel if they have the same slope. They can have different y-intercepts. So any line in the form
y = -2x/3 + b is parallel to the line 4x + 6y = 24 (even including b=8/3!!) In fact any line of the form 4x + 6y = C will work for any C.

 

[HallsofIvy]

There are an infinite number of lines parallel to the line given by 4x+ 6y= 8, all with slope -2/3 so all of the form y= (-2/3)+ b= \frac{-2x+ 3b}{3} where "b" can be any real number.

 

[lookagain]

Recall that two lines are parallel if they have the same slope. They can have different y-intercepts.

No, they *must* have different y-intercepts, else they are the same line.

So any line in the form
y = -2x/3 + b is parallel to the line 4x + 6y = 24 (even including b=8/3!!) In fact any line of the form 4x + 6y = C will work for any C.

That is except for C = 24. A line cannot be parallel to itself.

There are an infinite number of lines parallel to the line given by 4x+ 6y= 8, all with slope -2/3 so all of the form y= (-2/3)+ b= \frac{-2x+ 3b}{3} where "b" can be any real number.

That is except for b = 4/3, else it would be the same line.

 

[Steven G]

No, they *must* have different y-intercepts, else they are the same line.




That is except for C = 24. A line cannot be parallel to itself.




That is except for b = 4/3, else it would be the same line.

I disagree with you on your definition of parallel lines. Two lines are parallel if they have the same slope. They can be the same two lines.
I believe that two lines (in a plane) are parallel if they do not intersect OR they intersect everywhere on the line.

 

[tathagata7]

Hello all,

Thank you all for weighing in.

For the exam, what would be the best way to derive the answer?

Should I do the problem as I originally described?

Thanks!

 

[Steven G]

Hello all,

Thank you all for weighing in.

For the exam, what would be the best way to derive the answer?

Should I do the problem as I originally described?

Thanks!

If all the choices are in the form y =...., then do as you did and solve for y noting what the slope is. Then pick the choice that has the slope which you just found.

 

[lookagain]

I disagree with you on your definition of parallel lines.
Two lines are parallel if they have the same slope. They can be the same two lines.
I believe that two lines (in a plane) are parallel if they do not intersect OR they intersect everywhere on the line.

Parallel lines are two lines that are the same distance apart that never touch. Having the same slope is a necessary, but not a sufficient, condition.

 

[HallsofIvy]

I disagree with you on your definition of parallel lines. Two lines are parallel if they have the same slope. They can be the same two lines.

"The same two lines"? Do you mean "the same line"?

I believe that two lines (in a plane) are parallel if they do not intersect OR they intersect everywhere on the line.

But then you cannot say "two lines"- there is only one line.

The definitions of "parallel line" that I have always seen only say that the two lines do not intersect- NOT that the can intersect everywhere on the line.
For example, https://en.wikipedia.org/wiki/Parallel_(geometry), http://www.mathopenref.com/parallel.html,

http://www.wolframalpha.com/input/?i=parallel+lines&x=0&y=0 says only that "Two lines in two-dimensional space are said to be parallel if they do not intersect".

Do you have any authority for the idea that "two lines are parallel if they have all points in common" or, perhaps, "a line is parallel to itself?