Question

How do you graph a linear function? y = 1/5x -2 (1/5 is a fraction) I understand that the -2 is where the y intercepts on the graph, but I can never figure out the points from the slope. It's so confusing :/ @iGreen

Answer 1

there are two ways:
one way is find two points on the line, plot the points, and draw a line through them

Answer 2

to find a point, pick a number for x, "put it in" the equation, and figure out y
that will give you an (x,y) pair to plot

Answer 3

o.o ?

Answer 4

you already know (0,-2) is a point

Answer 5

ok so fractions are also known as rise/run so you always plot the y-intercept first which in this case is -2. Then because its rise over run you go up 1 and over 5

Answer 6

I would pick x=5 as a number to use, and figure out y

Answer 7

you can pick any x value, but x=5 gives a "nice y"
do 1/5* 5 and then add -2 to get y
(that is what
\[ y= \frac{1}{5} x -2 \]
is telling you to do ...

Answer 8

This is probably really easy but I'm so confused.

Answer 9

It is not so hard you can't learn it.

what is 1/5 * 5 ?

Answer 10

1?

Answer 11

yes
what you are doing is
y = 1/5 x -2
you picked x =5 and did
y= 1/5 * 5 -2
or
y= 1 -2

what is 1-2 ?

Answer 12

wouldn't that technically be 1 +2 because the 2 is negative and theres some kinda rule for that? So 3.

Answer 13

1-2= -1 but you don't have to solve for y to graph this.

Answer 14

you can think of
1-2 as the same as 1 + -2
either way, you don't get 3

Answer 15

you already know the y int is (0,-2).....you can find the x int by subbing in 0 for y in your equation

Answer 16

Oh oops. Haha. -1

Answer 17

here is the idea:
y = 1/5 x -2
is a recipe to find y. you "put in x" and get out y
do you follow that idea?
you found when x =5 then y is -1
or, as an (x,y) pair, you write (5, -1)

you now know
(0, -2) and (5.-1)
if you know how to plot points, you plot these, and draw a line between them

Answer 18

Is it this one?

Answer 19

here is how to plot points
https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-geometry-topic/cc-5th-coordinate-plane/v/graphing-points-exercise

Answer 20

lousy graph, but it looks about right.

Answer 21

It's not mine but.. yeah

Answer 22

that is graphed correctly and desmos is a great site to graph points.

Answer 23

the other way to do this problem is
plot (0,-2)
then look at the slope 1/5 which means move up 1 step (from the top number)
then move 5 sides (to the right) to get to another point on the line.

Answer 24

are these ideas hard to understand ? or is it you can't remember all the details ?

Answer 25

move up one step from 0?

Answer 26

Oh from -2?

Answer 27

from any point on the line. you know the y-intercept is -2, and that means
(0, -2) is a point on the line.
so use that point. move up 1 (you end up at y=-1) then sideways 5 steps, you end up at (5,-1)

Answer 28

Yeah. I can plot them once I know the points. I just have trouble finding the points for the slope :/

Answer 29

if you used (5,-1), the next "nice point" is at (10,0)
(but your answer graph does not show that point)

Answer 30

What if it was like y=-2x+3? Like a whole number?

Answer 31

there are two strategies. one way is use the slope idea (top number is how far to move up), bottom number how far to move sideways.

the other way is find a second point. if you have a fraction for the slope. pick an x that the bottom number of the slope divides into.
Example: slope is 1/5. pick x=5 because 1/5* 5 is a nice number

Answer 32

*** What if it was like y=-2x+3?****
first way: find 2 points.
(0,3) is the y-intercept.
I would pick a small x number. x=1 for example, and figure out -2*1+3
which is -2+3 or 1
(1,1) is the second point

Answer 33

Are you sure thats the right points though?

Answer 34

second way:
(0,3) is the y-intercept
slope is -2. write it as -2/1
that means move *down* 2 steps, then 1 step over
(1,1)

Answer 35

A line has lots and lots (infinite number) of points. All we want are two points, and draw a line through them. Then look at the graph to read off any point we want.

Answer 36

Okay.. I think? But so if theres like a whole number take /1 like and you go down two steps and one over from where y intercepts which would be three? That's a lot easier to remember haha

Answer 37

if the slope is 2, you would write it as 2/1
that means move up two steps, and over (to the right) 1 step

if the slope were -3, you would write it -3/1
down 3 , over 1

Answer 38

if the slope were -1/3
down 1, over 3

Answer 39

Yeah I get it.. Thank you so much!

Answer 40

It's really not *hard*, is it? and someday it might be useful. and in the meantime, it is practice learning and thinking

Answer 41

Yeah. Thanks!