Question

can someone help me understand how to get a system of equations from a graph?

Answer 1

the teacher won't explain it and the lesson doesn't help either

Answer 2

Do you mean like a solution to them? Or just how to find an equation for each?

Answer 3

just how to find them

Answer 4

Hopefully, the graph shows *straight lines*
does it ?

Answer 5

something similar to this

Answer 6

you need to find the equation of each line.

to find the equation of a line, the easiest way is to find
any two points on the line.
can you read off a point on one of the lines ?

Answer 7

i also have the curved line ones but i'll save that for later

Answer 8

the only point is (-1,-4)

Answer 9

lines have lots of points

Answer 10

oh that's what you meant

Answer 11

that is the graph but i just want to learn how to actually find them for later

Answer 12

ok (-1,-4) is on both lines (which means it is the solution)
for the lower line, can you figure out what it's "y" value is when x is 3 ?

Answer 13

(3,0)?

Answer 14

yes

now we have two points, (3,0) and (-1, -4)

Answer 15

so i find the slope?

Answer 16

we now find the slope between those two points

Answer 17

\[\frac{ -1-3 }{ -4-0 }\]

Answer 18

yes, and that simplifies to -4/-4 or just 1

Answer 19

1

Answer 20

oh you meant it simplifies to both

Answer 21

so the equation is y= mx + b
we found m=1, so y = 1*x + b
or (not bothering to show multiply by 1):
y= x+b
to find b, use (3,0) (or -1,-4)

Answer 22

wouldn't "b" be 3? because it's the y-intercept? or am i wrong

Answer 23

we can read off the y-intercept from the graph, but it is not 3

Answer 24

oh wait y-intercept is when x=0

sorry brain fart

Answer 25

y-intercept means where the line "intercepts" (fancy word for meets) the y-axis
y-axis is the vertical axis

Answer 26

using algebra and point (3,0)
0 = 3 + b
add -3 to both sides
-3+0 = 3+-3 + b
-3 = b
so b is -3
(and that is what the graph shows)
y= x - 3

now put this in standard form:
x - y = 3

Answer 27

-y=-x+3
and then divide the whole thing by -1?

Answer 28

yes you can divide by -1
but standard form is A x + B y = C
where A is positive
so I would add +x to both sides , to change
-y = -x +3
to
x - y = 3

that is probably the form they want for the equation
(variables in alphabetical order, first coefficient positive)

Answer 29

now find the equation for the steep line.
looking at the graph we see its "b" (y-intercept) is 3
so you just need the slope.

Answer 30

you can see the line moves "over 1" , and up 7
so its slope will be 7 (change in y divided by change in x)

Answer 31

okay i'm a little bit lost.... what do i do after i put it in standard form?

Answer 32

oh wait never mind i see what you mean

Answer 33

so the answer to this one would be 7x+3=x-3?

Answer 34

the second line will have an equation
y= 7x + 3
and in standard form
7x -y = -3

and the system of equations is
x - y = 3
7x -y = -3

Answer 35

to solve, we can subtract the two equations
x - y = 3
-(7x -y = -3)

x-7x -y +y = 3 - -3
-6x = 6
x= 6/-6
x= -1
(as we know it would be)

to find y, use either equation, with x= -1
example:
x - y = 3
-1 - y= 3
-y = 4
y = -4

Answer 36

okay i see that but how do i get an answer like x+4=x+5?

Answer 37

I think you are asking, How to solve the system of equations
One way is elimination (see my post up above)

the other way is substitution
if we write both equations in slope-intercept form:
y= x - 3
y = 7x + 3

the x-3 equals y
and 7x+3 equals y
so (where the lines meet and both lines have the same y value)
x-3 = 7x +3
you can solve for x by adding -x to both sides
x-x -3 = 7x -x + 3
-3 = 6x + 3

and you can finish solving ...

Answer 38

these are the answer choices they gave us

Answer 39

ok, then they must want
x-3 = 7x +3
or
7x + 3 = x - 3

Answer 40

so i was right?

Answer 41

yes, up above you picked that out.

notice we could have "cheated" by looking at the graph and seeing the solution
is at x= -1 (and we expect to find y= -4)

so if we put x=-1 into each choice, only one of them will show -4 = -4
after we simplify

Answer 42

so trial and error?

Answer 43

depends. If you get stuck on a question or are lost, then testing each choice is a different way to solve the problem.

Answer 44

okay so the first way is to find the slope and y-intercept and the second way is plugging in the numbers

Answer 45

yes

Answer 46

thank you phi.... can i bother you for one more type of graph?