Question

Write an equation in STANDARD FORM for the line that:
a) passes through the point (4,5) and has slope m=2/3
b) passes through the points (1,-6) and (-3,-9)

Answer 1

before we start, you have to learn some terms:
standard form for a line is \(Ax + By = C\)
vertex form of a line is \(y=mx+b\) , where m is the slope and b is the y-int
equation of a line is \((y-y_1)=m(x-x_1)\), where \((x_1, y_1)\) is any point in the line and m is the slope..


let's do letter a , first
so you are given the slope and a point
use the equation of the line
\((y-5)=(\frac{2}{3})(x-4)\)
can you simplify this equation?

Answer 2

y=2/3(x-4)+5
sorry im not really good at this unit

Answer 3

@Chibi_Robo3 ^^

Answer 4

yeah, that's great :)
but since we are looking for STANDARD FORM
we just have to leave it like this:
\(y−5=\frac{2}{3}x−\frac{2}{3}(4)\\y-5=\frac{2}{3}x−\frac{8}{3}\\y=\frac{2}{3}x−\frac{8}{3}+5\\y=\frac{2}{3}x+\frac{7}{3}\)
arranging and simplifying this equation, you'll get:
\(3y=2x+7\) -> multiply both sides by 3 to remove fractions
\(2x-3y=-7\) -> standard form \(ax + by= c \) ☺

Answer 5

oh okay so 2x-3y=-7 is the answer for part A ?

Answer 6

for the next one
you have to find the slope (m) using the slope formula:
\( \LARGE m= \frac{Δy}{Δx}=\frac{y_A-y_B}{x_A-x_B} \)
where \((x_A, y_A)=(1,-6)\) and \((x_B, y_B)= (-3,-9)\)
can you solve for the slope?

after you find the slope, do the same process as I did before for part A

and yes:)

Answer 7

okay so i'd be doing the y2-y1/ x2-x1 strategy right?

Answer 8

so -9-(-6) / -3-1

Answer 9

= -9-(-6)=-3

Answer 10

and -3-1= -4

Answer 11

so m= -3/-4

Answer 12

yea that's all i know for that part because i'm not sure if i have to find B or not

Answer 13

you don't need to find b , since we are looking for the standard form, you can just use the equation of a line

Answer 14

so would i do this? :
y=mx+b
y=-3/-4x+b
(1,-6)
-6=-3/-4x+1+b
b= -6-(-3/-4)(1)

Answer 15

i get stuck on that part because i dont know how to subtract and multiply for that part

Answer 16

and im not sure if im following your steps properly lol

Answer 17

for m , you got it right
m=3/4

hmm..it's the same thing but i guess you understand the other one, so let's stick with your method:)
what did you get for b then?
(1,-6)
\(y=\frac{3}{4}x+b\\-6=\frac{3}{4}(1)+b\\b=\frac{3}{4}+6\\b=?\)

Answer 18

b= 9/4

Answer 19

right?

Answer 20

i got a different answer for b

Answer 21

oh then i probably got it wrong...what was your answer

Answer 22

27/4

Answer 23

oh okay then i'll just go with your answer as b

Answer 24

but how did you get 27/4

Answer 25

like was it using your way?

Answer 26

@Chibi_Robo3 ^

Answer 27

oh okay i believe i understand what you did.... so you multiplied 6x4 and then added 3 and got 27/4

Answer 28

now that i understand...how can i put that into standard form?

Answer 29

you have \(y=\frac{3}{4}x+\frac{27}{4}\)
to change this vertex form to standard form
multiply both sides by 4, to remove fractions, what will you get?

Answer 30

how do i do that ?

Answer 31

just multiply each term by 4