Question

I am confused about graphical transformations on linear equations. Do we still use the y=mx+b formula? Can someone show me an example?

Answer 1

No. If you're trying to find a translation, or dilation, etc... you use differen't formulas. y=mx+b is finding linear equations.

Answer 2

If you're finding transformations, they're differen't

Answer 3

I think...

Answer 4

so what is some examples of the other formulas?

Answer 5

Like... for dilations, you need to figure out how to make it larger, technically, you just find what k=... and then multiply

Answer 6

for example -2,7

Answer 7

and if k=3

Answer 8

it would be -2 time 3 and 7 time 3

Answer 9

y=mx+b is basically invalid

Answer 10

it all depends on whether you want to make it smaller or larger

Answer 11

Yeah...

Answer 12

now im more confused.. :(

Answer 13

m is the slope, when it is positive, the function is increasing, and when it's getting bigger, the slope becomes more and more vertical.
y = mx + b
b is the y-intercept, it translate the function upward or downward

Answer 14

so you do still use the formula?

Answer 15

Let me give you some examples;
Let's say we have this very basic function, y = x
http://puu.sh/s8N7

Answer 16

If we change the slope to 2, http://puu.sh/s8Nl
It would be like this.

Answer 17

If you want to translate the function upward, let's add something to our function, y = 2x + 5
so our y-intercept would be at 5
http://puu.sh/s8O0

Answer 18

and say the slope was -2? it would go the opposite way? or would that make it a reflection?

Answer 19

If the slope is -2, let's compare
y = 2x and
y = -2x
http://puu.sh/s8Ox
In this case, you can say that the function is reflected on the x-axis.

Answer 20

When the slope is positive, the function is strictly increasing, and when the slope is negative, the function is strictly decresing. :)
Have any other questions?

Answer 21

oooh thanks that makes it a lot more clear. yes does linear have like stretches or shrinks?

Answer 22

like some other functions do

Answer 23

no you use the transformation rules:

Answer 24

If the slope's value is getting bigger and bigger, we can say that the function has been streched, yes.

Answer 25

and you don't 'really' need to learn the rules that babarica posted by heart, since this is all about observations, but it is still helpful if you need references :)

Answer 26

okay thanks so w what you said about stretching if the slope gets bigger..would it be compression if the slope gets smaller?

Answer 27

Yes, in fact, the absolute value of the slope getting bigger = stretch
If we have y = -2x and y = -5x
The function has been streched, even though -5 is smaller than -2, so we have to take a absolute value of the slope to compare.

Answer 28

oooh okay makes sense thanks soo much for your help Zepp! :)

Answer 29

Here: http://puu.sh/s8Vg

Np ;)

Answer 30

thanks!