Question

Write an equation of the line containing the given point and parallel to the given line.

(5,-6); 4x-5y=9

the equation of the line is y=

Answer 1

so first put it into slope intercept form which is y=mx+b

Answer 2

i dont know how to do that :/

Answer 3

took me a while too :)

so you want to isolate the y

Answer 4

start by subtracting the 4x from both sides this cancels it out on the left hand of the = sign and puts it on the right with the 9 like so
-5y=9-4x

Answer 5

you can then rearrange to make it look more like the final result giving yourself
-5y=-4x+9 this works for aesthetics but if the (-) sign gets overwhelming you can wait until later too

Answer 6

kk thank you, and i think you divide both sides by -5

Answer 7

Yup then divide both by -5 and you can keep it as
y=\[\frac{ 4x-9 }{ 5 }\] or make it
\[y=\frac{ 4 }{ 5}x-\frac{ 9 }{ 5}\]
whichever is easier for you to understand
I personally understand the 2nd one better

Answer 8

The second part is finding a line parallel which uses the same slope in this case \[\frac{ 4 }{ 5 }\]

Answer 9

to have it go through the point given you just put those into your equation of
\[y=\frac{ 4 }{ 5}x+b\]
so x=5 and y=-6
this gives you
\[-6=\frac{ 4 }{ 5}*5+b\]
solve for b

Answer 10

kk thank you!! i really apreciate it :)

Answer 11

b=-10
so final answer should be \[y=\frac{ 4 }{ 5 }x-10\]
no problem! Glad to help

Answer 12

do you need help with a perpendicular one too?

Answer 13

no just with the equations for now :)