Math nerds: working out if 2 line slopes are perpendicular

[thecat]

Hi all.

having a bit of trouble helping my daughter with her math homework.

Basically working out if 2 lines a perpendicular from their equations. Now my some what addled memory with some google checking says that for line y=mx+b m is the slope and b is the m̶a̶d̶ ̶m̶a̶x̶ intercepter and two lines are perpendicular if and only if m1= -(1/m2)

Now first question is to compare y=4 and y=1/4x-2
so does 4=-(1/1/4) 1/1/4=4 so we have
does 4=-(4) no. so I would say the lines are not perpendicular but the answer in back of book says yes they are with no explanation.

Have I completely misunderstood something?

Next question is even worse as it asked to compare y=3 and x=4 to see if they are perpendicular. Now have I lost the plot or is y=3 and x=4 both points not lines and so can't be perpendicular? Because the answer says they are, again with no explanation

 

[Dales Cannon]

For lines to be perpendicular m1 * m2 = -1 as you have stated. So y=4 is a line parallel to the y axis and as it has no x term the slope is 0. As in y=0x + 4. The other line has a slope of 1/4 so no they are not perpendicular. 0 * 1/4 = 0 and not -1. If the answer is yes are you sure the equation isn't y=-4x?

y=3 is again a line parallel to the y axis and x= 4 is a line parallel to the x axis. As the x and y axis are perpendicular to each other so too are these lines. Any point has two coordinates not one so a point would be (say) 2,3 while y=3 is a line.

KO?

 

[thecat]

For lines to be perpendicular m1 * m2 = -1 as you have stated. So y=4 is a line parallel to the y axis and as it has no x term the slope is 0. The other line has a slope of 1/4 so no they are not perpendicular. 0 * 1/4 = 0 and not -1.

y=3 is again a line parallel to the y axis and x= 4 is a line parallel to the x axis. As the x and y axis are perpendicular to each other so too are these lines. Any point has two coordinates not one so a point would be (say) 2,3 while y=3 is a line.

KO?

Champion

So first one the text book had wrong. Second was purely me. No wonder my daughter is confused. Thanks heaps

 

[Dales Cannon]

Check my edit maybe the first equation is y=-4x????

 

[thecat]

Check my edit maybe the first equation is y=-4x????

No I double checked that first but I'm guessing it was suppose to

 

[bell.cameron]

For a line to be perpendicular it basically has to have the opposite gradient yeh? so if the gradient of line a=4 then the gradient of line b must = -1/4. The location of the y intercept is irrelevant. I have always found this the simplest way unless you're dealing with vectors. So basically if the gradient of a= x the gradient of b = -1/x

 

[andy]

For lines to be perpendicular m1 * m2 = -1 as you have stated. So y=4 is a line parallel to theto the x axis y axis and as it has no x term the slope is 0. As in y=0x + 4. The other line has a slope of 1/4 so no they are not perpendicular. 0 * 1/4 = 0 and not -1. If the answer is yes are you sure the equation isn't y=-4x? (The rest is correct

y=3 is again a line parallel to the y axis and x= 4 is a line parallel to the x axisThe other way around . As the x and y axis are perpendicular to each other so too are these lines. Any point has two coordinates not one so a point would be (say) 2,3 while y=3 is a line That has many coordinates.

KO?

Interestingly check that they only call them equations as y=3 is a Function but x=4 isn't.

 

[driftking]

When in doubt graph it out.

For any equation
Say y=1/4x-2

You can easily create a table is say
X Y
1
2
3
4

And run through each equation and graph it.
So for y=1/4x-2
X Y
1 Y=1/4(1)-2 1.75
2 Y=1/4(2)-2 1.50
4 Y=1/4(4)-2 1.00

So once you graph that out you now how two points. when X=1 Y=1.75, when X=4 Y=1 etc so these are now plot points.
Plot them out and draw a line through the points.

For Y = 4 there is no value for x so therefore x=0 there is no input for x. as you cans ee below there is no substitution for x so y=4 always no matter what x is y always equal 4.

X
1 y=4
2 y=4
4 y=4

On graph that would be a straight line though Y=4


No matter what value you give X if you draw a line that reaches x=400 and every time y=4 so it graphs a straight line.

If we plot the first line on here too of y=1/4x-2
You get (forgive my dodgy inaccurate drawing)


It clearly does not intersect at a perpendicular angle.

For y=3 x=4

There again is no other value so y is intersected at 3 at a straight line parallel to the x axis and x is a straight line intersecting 4 parallel to the y axis. At some point these lines will intersect at a 90degree angle and therefore yes are perpendicular.

If you graphed these both out it would be the same deal as before in where for y=3 no matter what the x value is y will always be 3 and for x=3 no matter how far you go up or down the y axis x always equals 3 at some point in the infinite lines they will intersect perpendicular to each other.


Please someone correct me if any of this is wrong.

 

[driftking]

Interestingly check that they only call them equations as y=3 is a Function but x=4 isn't.

why cant x=4 be a function.

You could technically have x=1/4y-2 in which case x would be a function would it not.
Y and x technically have no value except the value the equation is given to them so you could use each interchangeably as a function or a equation?

you could easily have y=F(x) or x=F(y)

 

[thecat]

Thanks all.

It would have to be the worst resource book I've come across. Just a bunch of questions and final answers without examples on what they are asking nor explanations on how the final answer is arrived at.

From what I could tell it wanted the calculations without graphing it. Then again I could be wrong as they hadn't covered it in class and, as I said the book gave no indication.

I'm going with the first question had a typo as we've got the following ones sorted after dales clarification

 

[Dales Cannon]

Sorry cat, cocked up the x and y (obviously just wrote out the answer off the top of my head) but the guts of it was right advice.

 

[andy]

why cant x=4 be a function.

You could technically have x=1/4y-2 in which case x would be a function would it not.
Y and x technically have no value except the value the equation is given to them so you could use each interchangeably as a function or a equation?

you could easily have y=F(x) or x=F(y)

Because the definition of a Function is that the Domain can only have one Range. With x=4 the coordinates for example in quadrant one would be (4,0) (4,1) (4,2) etc. Also if obviously fails the vertical line test since it is a vertical line.

 

[andy]

Sorry cat, cocked up the x and y (obviously just wrote out the answer off the top of my head) but the guts of it was right advice.

Absolutely. Figured as much as your explanation is quite good.

 

[thecat]

Sorry cat, cocked up the x and y (obviously just wrote out the answer off the top of my head) but the guts of it was right advice.

Yeah got that. Your explanation got me on the right track and sorted it out in my brain thingie