Question

What is the solution to the system?

Line 1
x y
–1 9
3 –3
Line 2
x y
–1 –1
2 5

( , )

Answer 1

@hartnn

Answer 2

@zepdrix

Answer 3

@bibby

Answer 4

@mathmath333

Answer 5

These are lines? Just straight lines?
So we can use our handy approaches to come up with equations for each line.

Answer 6

yes

Answer 7

Given the data for the first line, \(\Large\rm (-1,9)\) and \(\Large\rm (3,-3)\),
Our slope formula gives us:\[\Large\rm m=\frac{y_2-y_1}{x_2-x_1}=\frac{-3-9}{3--1}=\frac{-12}{4}=-3\]So the slope of that first line is -3.\[\Large\rm y=mx+b\]\[\Large\rm y=-3x+b\]To find the y-intercept, let's plug one of the points in and solve for b.\[\Large\rm 9=-3(-1)+b\]Solving for b gives us b=5.

So the equation of our first line is, \(\Large\rm y=-3x+5\).

Answer 8

Do you understand the process? :o
Think you can apply that to the second set of data?

Answer 9

Woops :) Not b=5, I shoulda said b=6. hehe was moving too fast.

Answer 10

i know how to fid the slope but i dont understand how to find the y intercept

Answer 11

find*

Answer 12

What's the slope of the second line?
Take a minute to calculate it :3 imma go grab a drink real quick

Answer 13

the slope is 6/3 for line 2

Answer 14

Mmmm ok very good.\[\Large\rm y=2x+b\]

Answer 15

So we have a line,\[\Large\rm \color{orangered}{y}=2\color{royalblue}{x}+b\]And to find the y-intercept, we need to plug in a point that the line passes through.
Let's use this point which was given to us: \(\Large\rm (\color{royalblue}{x},\color{orangered}{y})=(\color{royalblue}{2},\color{orangered}{5})\)

Answer 16

Do you see WHERE we'll plug the values in?
I tried to color code them.

Answer 17

5=2(2)

Answer 18

5x=2(2)

Answer 19

We're not plugging anything in for the b, so don't let that part just disappear.\[\Large\rm \color{orangered}{y}=2\color{royalblue}{x}+b\]\[\Large\rm \color{orangered}{5}=2\color{royalblue}{(2)}+b\]

Answer 20

ok

Answer 21

5=4+b

Answer 22

mhm, solve for b.

Answer 23

but how thats what im confused about?

Answer 24

To isolate the b, we're just applying a simple algebra step.
The 4 is being ADDED to the b,
We want to apply the inverse operation to get the b alone.
So we'll SUBTRACT 4 from each side, yah?