Question

Write the point slope form of the equation of the line described

through (4,2), and parallel to y=-3/4x-5

I really don't get this can someone help :/

Answer 1

can you identify the "slope" of the equation y=-3/4x-5?

Answer 2

@kaiters1010 what happens to the 5 :?

Answer 3

we are not changing the equation y=-3/4x-5,
so nothing is gonna happen to 5.

we are tying to find the equation of another line parallel to line y=-3/4x-5

so it will be in the form of
y=-3/4x+c
and we need to find the 'c'

we can use the information that 4,2 lies on the line y=-3/4x+c

so plug in x =4, y =2 in that

2 =-3/4* 4 +c
!
once you get the 'c' , you get the equation

Answer 4

and c is gotten like y=x+b correct?

Answer 5

you mean y = mx+b ?

here m is the slope , b is the y-intercept.

we have slope = m= -3/4 here

can you try to solve
2 =-3/4* 4 +b
to get the value of the y-intercept 'b' ?

Answer 6

b=-1

Answer 7

how did you get that??

2 = -(3/4)*4 + b

2 = -3 + b

now add 3 on both sides :)

Answer 8

Oh which it would be 1 not negative

Answer 9

actually, lets do it step wise,

2 = -3 + b

2+3 = -3+3 +b

5 = 0 + b

so b= 5

makes sense?

Answer 10

Yes It did in the beginning I mixed up on the negative positive bit.

Answer 11

so finally, we have the equation as

y = -3/4 x + 5 :)

Answer 12

ahh, just read the question, we need the equation in "point-slope" form!

which is

\(y = y_1 = m (x-x_1)\)

and the point \(x_1, y_1 = 4,2 \)

so the same equation would be
\(y - 2 = -(3/4) (x- 4)\)

Answer 13

***
\(\Large y \color{red}-y_1 = m (x-x_1)\)

Answer 14

So x1 nd y1 is the one i got from the one that is parallel ?

Answer 15

x1 and y1 are the co-ordinates that are given to you : (4,2)

Answer 16

confused?

Answer 17

(4,2) = (x1,y1)

Answer 18

then what about y and x I'm getting really confused :/

Answer 19

Would the solution be y−2=3/4(x−4)

Answer 20

y−2=-3/4(x−4)

Answer 21

I see and would that end of the question because it got very simple now

Answer 22

yep, thats all we had to do,
find the slope, which was -3/4

and plug in the point!
x1 = 4, y1 =2

Answer 23

So basically the point slope form would be y-2=-3/4(x-4

Answer 24

yes

Answer 25

Ok I got 3 more questions I'll try to do myself if I have any questions would it be ok to tag you :?

Answer 26

sure :)