Question

What is the equation of the graphed line?

Answer 1

@phi

Answer 2

can you list two points on the line ?

Answer 3

7 and -6?

Answer 4

these are the answer choices
a: y=6x
b: y=1/6x
c: y=-1/6x
d:y=-6x

Answer 5

a point is an (x,y) pair. for example, when x is 6 (move to the right till you get to 6), then move up until you reach the line. How many steps up do you move ?

Answer 6

1?

Answer 7

yes. that means (6,1) (that is the x and y numbers) is a point on the line
can you find another point ?

Answer 8

y?

Answer 9

look for a spot where the line goes through where two lines cross (this will give an easy number to read)

Answer 10

-1 and 6?

Answer 11

Here are 3 points that we can "read off"

Answer 12

ok

Answer 13

can you figure out the x and y for the "middle point" ?

Answer 14

the third point is zero i believe

Answer 15

yes, but think (x,y) pair. what number is x and what is y ?

Answer 16

y is -6 and x is 6

Answer 17

x = 6 and y=-6 is here

Answer 18

alright

Answer 19

If you have time, see this for how to find point on a graph
https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-geometry-topic/cc-5th-coordinate-plane/v/graphing-points-exercise

Answer 20

meanwhile, the other two points on the line that are easy to read are
way on the left. x is -6 and y is -1 (-6,-1)
the middle point is at x=0 and y=0 (0,0)

Answer 21

so do we divide anything?

Answer 22

now that we have two points
(0,0) and (6,1)
we can find the equation of the line.
The first step is find the slope. Do you know how to do that ?

Answer 23

slope is change in y divided by change in x

Answer 24

so we change the points?

Answer 25

change in y means find the difference between the y values of the two points.

Answer 26

I would pick out the y values and get 0 (from (0,0)) and 1 (from (6,1))
and find the difference
1 - 0 = 1

Answer 27

can you find the change in x ?

Answer 28

6-0=6?

Answer 29

yes.

so we know "change in y" is 1 and "change in x" is 6
slope is "change in y" divided by "change in x"
what is the slope for our line ?

Answer 30

1/6?

Answer 31

yes

we are going to write the equation in "slope-intercept" form
y = m x + b
where m is the slope
we found m= 1/6 so we can write
\[ y = \frac{1}{6} x + b \]
b is the y-intercept (the y value where the line crosses the y-axis)
if you can't tell from the graph, we can use either point, to find "b"
Let's use (0,0)
0,0 means x =0 and y =0. Use those numbers in the equation
y = 1/6 x + b
0 = 1/6 * 0 + b
what is b ?

Answer 32

y= 1/6x?

Answer 33

b=0 so the equation could be written
y = 1/6 x + 0
but we don't bother to write +0 (adding 0 doesn't change anything)
so yes,

y = 1/6 x

Answer 34

so that's the equation for this graph?

Answer 35

yes.

y = 1/6 x
gives us the points on the line
for example, when x is 0 we get
y = 1/6 * 0 which simplifies to y=0 so (0,0) is on the line

or if x=6 we find y= 1/6 * 6 = 1 so (6,1) is on the line.

or if x=1, y = 1/6*1 = 1/6 and (1, 1/6 ) is on the line
notice that "reading off" 1/6 for the y-value on the graph is hard to do.

Answer 36

thank you very much :)