Question

On graph paper, graph y = (2/7)x – 2. Explain how to graph the equation using the slope and y-intercept.

Answer 1

@freckles

Answer 2

y=mx+b
tells us the slope is m
and the y-intercept is (0,b)

So can you first identify the slope and the y-intercept ?

Answer 3

m=27,b=−2 where m is the slope and b is the y-intercept

Answer 4

m=2/7 and b=-2
so the slope is 2/7
and the y-intercept is (0,-2)

So your job is to first plot the point (0,-2)
this just a point on the y-axis 2 units below the origin

Answer 5

after you plot this point we will use m=2/7 to find one more point

slope is rise/run
so what m=2/7 tells us is we are going to start from our (0,-2)
and count up 2 units from then count right 7 units

Answer 6

and that will be another point on the line
then connect the dots and you have your line

Answer 7

so basically if you have (x,y) on the line then
(x+7,y+2) will also be on the line

Answer 8

so since you have (0,-2) on the line then what other point can you say is on the line?

Answer 9

(2,5)??

Answer 10

So
we have (x,y) then (x+7,y+2)
you have (0,-2) then (0+7,-2+2) right?

Answer 11

ya

Answer 12

so that means plot both points (0,-2) and (7,0) and connect the dots

Answer 13

okay :) could you help me on one more?

Answer 14

ok I can try

Answer 15

On graph paper, graph the line containing the point (–6, 6) and having a slope of m = –3/2. What are the coordinates of a second point that is located on the line?

Answer 16

pretend just like before we know we have a line
and we know the point (x,y) is on there and we the slope is b/a
what the slope means is we are going to move (x,y) up b units and right a units (assuming a and b are positive)
so you will have the point (x+a,y+b) also on the line

as you can see if we do
\[\frac{(y+b)-y}{(x+a)-x}=\frac{b}{a}\]
which was indeed the slope we had for this example



if you have point (x,y) on the line then you also have if the slope is b/a then the point (x+a,y+b) is on the line

Answer 17

so you have
\[\frac{-3}{2}=\frac{b}{a}\]
b=-3 and a=2
so if (-6,6) is on the line then what other point is also on the line?

Answer 18

(-9,-8)

Answer 19

let see (x,y) -> (x+a,y+b)
a=2 and b=-3
x=-6 and y=6
so we have
(-6,6) -> (-6+2,6+(-3))

Answer 20

-8,3)

Answer 21

-6+2 is -4
:p

so you have another point on the line is (-4,3)

Answer 22

now I'm not saying these are the only two points on the line
it is just another way to find anther point

Answer 23

anyways plot (-6,6) and (-4,3)
and connect the dots

Answer 24

and you know you should continue the line past the points
after all it is a line
lines go in both directions forever and ever

Answer 25

thank you for your help:D