Question

Find an equation of the line. Write the equation using function notation.
Through (-6,-9); parallel to 5x+6y=11
f(x)=

Answer 1

@johnweldon1993 Please :(

Answer 2

Alright first things first...lets get the line you have into slope-intercept form

\[\large y = mx + b\] that one lol where 'm' is the slope...and 'b' is the y-intercept

5x + 6y = 11

subtract 5x from both sides

6y = -5x + 11

And divide everything by 6

\[\large y = -\frac{5}{6}x + \frac{11}{6}\]

This is the equation of your other line

So...what do we know about parallel lines in terms of slopes?

Answer 3

They are quite complicated...
And 2 fractions :)

Answer 4

Lol :P

Alright...well...we know the the slopes of parallel lines...are the same correct? If they were not...they would cross and not be parallel

So

If the slope of the line we have....is -5/6 then the slope of the line we want...is also -5/6

Make sense so far?

Answer 5

yes so the first fraction is -5/6 ?

Answer 6

Correct....

okay now..we need to introduce another form...called the point slope form

why? well it will tell us the equation of a line...if we have a point...and a slope :P

lol which we do...we are given a point and we just found the slope

so it looks like

\[\large y - y_0 = m(x - x_0)\]

same thing here...m = slope....so it will be the -5/6 we had

Answer 7

gotcha

Answer 8

and the \(\large (x_0 , y_0)\) will be replaced by your point \(\large (-6,-9)\)

so altogether we will have

\[\large y - (-9) = -\frac{5}{6}(x - (-6))\]

still with me there?

Answer 9

yes

Answer 10

So lets simplify it a bit, distribute the -5/6 into the parenthesis

\[\large y + 9 = -\frac{5}{6}x - 5\]

Then just subtract 9 from both sides

\[\large y = -\frac{5}{6}x - 14\]

and there we have our equation :)

Answer 11

thank you so much i really appreciate it!

Answer 12

Anytime :)

Answer 13

do you wanna help me with one more or nah?

Answer 14

nah ;P lol no jk go ahead :)