Question

Find an equation for the line with slope m through the point (a,c).

***I'm just forgetting some of the small steps... Could someone please refresh me? I know you start off with y=mx+b... I just forgot how to create the equation when you're using variables! THank you!!!:)

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1\\
&({\color{red}{ a}}\quad ,&{\color{blue}{ c}})\quad
\end{array}
\\\quad \\

slope = {\color{green}{ m}}
\\ \quad \\

y-y_1={\color{green} m}(x-x_1)\) plug and chug, and solve for "y"

Answer 2

ohhh so you're using point slope form for this one?

Answer 3

Well lets start from the easiest part - slope - this is the multiplier of the x

As such your equation becomes y = mx + T where t we need to find out.

since the line passes through point (a,c) then you know that when x = a, y =c

as such c = ma + t - all thats left is solve for T

Answer 4

so y-c=m(x-a) ?

Answer 5

yes, to get the equation, yes, you'd use the point-slope form

Answer 6

yeap

Answer 7

so do i distribute now?

Answer 8

and you can solve that for "y" to set to slope-intercept form

Answer 9

okay, so now it's y-c=mx-ma ?

Answer 10

@Garm when you say t, do you mean the y-int? :/

Answer 11

T is just unknown like x

Answer 12

solving for t and then substituting it into previous equation will yield an answer

Answer 13

ohhh i see :)

and @jdoe0001 how do we solve for the "y" ?

Answer 14

add "c" to both sides

Answer 15

turn formula into something that looks like y=.....

Answer 16

okay, just want to make sure i'm following correctly so far :)

are these the correct steps so far?

y-y1=m(x-x1)
y-c=m(x-a)
y-c=mx-ma
+c +c
=
y=mx-ma+c

??

Answer 17

did I do that last part right? :/

Answer 18

yes

Answer 19

okay awesome!! :)

do i do something after that? or is that the final equation? :/

Answer 20

well you know m a and c as such you have nothing else unknown in your equation but x and y - therefore it is a valid formula to draw a line =)

Answer 21

essentially that is what you are looking for - you need to make sure you only have 2 unknowns for function

Answer 22

how do i do that?

so from y=mx+ma+c, what do I do?

Answer 23

well what else you dont know in that formula but x and y?

Answer 24

we don't know m ? a and c?

Answer 25

you do

Answer 26

did I do that last part right? \(\large \checkmark\)

Answer 27

m a and c were given to you in the question

Answer 28

as such they are not unknowns they are essentially just abstract numbers

Answer 29

ohhh haha okay

but y=mx-ma+c has to be simplified more? am I understanding that right? or is that the final equation?

Answer 30

@jdoe0001 yes all your stuff is top notch

Answer 31

^^agreed :P and i love the latex! i can never remember how to do the latex stuff haha

Answer 32

@iheartfood nope! =) that's the beauty of algebra - you dont need to know the answer as number to actually have correct answer.

Answer 33

awesome!! so the problem is done?! :O

it's just y=mx-ma+c ?

Answer 34

indeed - because you cannot simplify it further.

Answer 35

okay great!!! :)

thank you so much!! @jdoe0001 @Garm I had totally forgotten how to do this with variables and this cleared it up! Thanks again :)

Answer 36

yw