Question

a line that passes through (1, 7), (10, 1)

Answer 1

find equation?

Answer 2

first we need the slope of the line
any ideas how to find the slope?

Answer 3

i have no idea srry

Answer 4

y-y1/x-x1 = y2-y1/x2-x1
y-7/x-1 = 1-7/10-1
y-7/x-1 = -6/9
y-7 = -6x/9 +6/9
y=-6x/9 + 23/3

Answer 5

\[\text{ given two points} (x_1,y_1) \text{ and } (x_2,y_2) \text{ on a line }\]
\[\text{ we can find the slope of that line and we will use m \to denote the slope of that line}\]
\[m=\frac{y_2-y_1}{x_2-x_1}\]

Answer 6

y=-2/3x+ 23/3

Answer 7

ooh ok I think I get it

Answer 8

\[m=\frac{7-1}{1-10} \]

Answer 9

So the slope would be 6/9?

Answer 10

it doesn't matter if you chose your points the other way by the way
almost

Answer 11

karate chopper simplified it 2/3

Answer 12

the opposite of 6/9

Answer 13

and it can be reduced like others are suggesting

Answer 14

the point to highlight is 1-10 in the denominator is -9, not positive...

Answer 15

happy boxing day, andy warhol

Answer 16

\[y=-\frac{2}{3}x+b\]
so this is how much we know about the line now

Answer 17

but what is that b

Answer 18

that b is the y-intercept

Answer 19

thats the only thing left to find

Answer 20

you find b by pluggin' a point on the line (two points are given to you either point is fine to use)

Answer 21

\[y=-\frac{2}{3}x+b\]
we know a point (1,7)
where x is 1 and y is 7
so we plug these into the equation
\[7=-\frac{2}{3}(1)+b\]
and solve for b

Answer 22

\[7=\frac{-2}{3}+b\]

Answer 23

how do you solve this for b?

Answer 24

you plugin 1?

Answer 25

she plugged in the 1 already
that's how you got the expression above
so can you solve what is above for b ?

Answer 26

I don't know sorry.. plugin 2?

Answer 27

you don't need to plugin anything, just solve it

Answer 28

it's just linear equation, i believe you solved many of them

Answer 29

linear equations r fun

Answer 30

no i plugged in 1 for x and 7 for y since we have a point on the line called (1,7)
1 is in the x place
7 is in the y place
so i just replaced them in the equation
y=mx+b
7=m(1)+b
7=m+b
so I want you to solve this for b by subtracting m on both sides
7-m=b
b=7-m

Answer 31

yes^

Answer 32

ooh..

Answer 33

\[b=7-(\frac{-2}{3})=7+\frac{2}{3}\]
so we found our equation of the line
y=mx+b
\[y=-\frac{2}{3}x+(7+\frac{2}{3})\]
I will leave the simplifying to you

Answer 34

Ok

Answer 35

You don't need those parenthesis there
i just wanted to be clear what I was saying b was

Answer 36

Ok, thank you