Question

find an equation of the line having the given slope and containing the given point.
m=2/3, (1,-2)

Answer 1

IMPORTANT LINE RELATED EQUATIONS TO KNOW AND MEMORIZE

slope formula
m= slope/ gradiant -- same thing
\[m=\frac{y_2-y_1}{x_2-x_1}\]

standard formula
\[Ax+By=C\]

point-slope formula
\[y-y_1=m(x-x_1)\]

slope-intercept formula
b= y-intercept -- in the form of (0,y)

\[y=mx+b\]

Answer 2

my book told me the answer was y=2/3x+-8/3 but i keep getting y=2/3x+4/3

Answer 3

take the slope and the point and substitute them into the point slope form

then convert that into the slope intercept or standard

Answer 4

one second while i check

Answer 5

y+2 = 2/3 ( x-1)

Answer 6

book is right, double check your steps

Answer 7

@completeidiot for the pint slope formula do i only fill in one of the x's and y's because i only have one set coordinates

Answer 8

yes you fill in y1 and x1

you leave x and y as variables

Answer 9

so would it be y--2=2/3(x-1) ?

Answer 10

yes

when you subtract a negative number, it is the same as adding the positive number

so your equation will look like

y+ 2 = 2/3 (x-1)

Answer 11

ok so now what do i do from there?

Answer 12

you should distribute first

Answer 13

please write down what you get

Answer 14

what do you mean distribute, do you mean the 2/3 to the x and -1

Answer 15

yes

Answer 16

distribution property of multiplication

a(b+c) = ab + ac

Answer 17

ok so i got y+2=2/3x -2/3 ( im not very good at adding and subtracting fractions so im not sure if i did that right)

Answer 18

ok you distributed correctly

now you want to convert it to slope intercept form

this can be done by subtracting 2 to each side

Answer 19

however, you cannot directly subtract 2 from -2/3 because they have different denominators

this mean you need to convert 2 into a fraction, this can be done by multiplying 1 to it or 3/3

Answer 20

\[2*1= 2 \]
\[1 = \frac{3}{3}\]
\[2 * \frac{3}{3} = \frac{ 6}{3}\]

Answer 21

so 2/3-2 is 6/3?

Answer 22

no

Answer 23

\[2 = \frac{ 6}{3}\]

Answer 24

so
substituting 2 for 6/3
the equation now looks like

y + 6/3 = 2/3 x - 2/3

Answer 25

now, we subtract 6/3 to both sides

Answer 26

y = 2/3 x - 2/3 -6/3

Answer 27

now,

\[-\frac{2}{3} - \frac{ 6}{3} = ?\]

Answer 28

-8/3

Answer 29

yes

Answer 30

any questions?

Answer 31

nope, thank you so much!!!!