Question

how do you find the equation for a line that passes through two coordinates (2,1), (5,3)?

Answer 1

what is the slope of the line connecting those two points?

Answer 2

there isn't a slope

Answer 3

the options are
3y=2x+1
3y=2x-1
3y=-2x-1
3y=-2x+1

Answer 4

im not telling you the answer im trying to show you how to get it.
what is the slope of the line through the two points listed?
y_1-y_0/x_1-x_0

Answer 5

3/4

Answer 6

(2,1) and (5,3)
\[\frac{3-1}{5-2}=?\]

Answer 7

2/3?

Answer 8

Lack of confidence is disturbing :)
Given two points, the slope is "difference of the y's divided by difference of the x's" :D

Answer 9

yes 2/3
ok so we know it has the form y=mx+b where m is slope so
y=2/3x+b right?

Answer 10

yes

Answer 11

right

Answer 12

Okay, whenever you have a slope \(\large \color{blue}m\) and a point \(\large (\color{red}p \ , \color{green}q)\)
The equation of the line having that slope and passing through said point is given by:
\[\Large y = \color{blue}m(x-\color{red}p)+\color{green}q\]

You may use any one of your two given points for \(\large (\color{red}p \ , \color{green}q)\)

Answer 13

none of this makes sense.

Answer 14

Okay... simply put... choose a point from the two that you were given. It doesn't really matter which, just choose one.

Answer 15

another method you could use is;
to plot the points
draw the line
and determine the equation from the picture

Answer 16

another method you could use is; to plot the points and draw the line and determine the equation from the picture

Answer 17

Well, anyway, once you've chosen from those points, the left coordinate would be \(\large \color{red}p\) and the right coordinate would be \(\large \color{green}q\).
You already have your slope \(\large \color{blue}m\).
So just plug them into this equation and simplify:\[\Large y = \color{blue}m(x-\color{red}p)+\color{green}q\]