what methods are useful to create the equation of a line? Demonstrate by writing an equation in standard form parallel to y=3x+2 through the point (5,-6)

Question

johnweldon1993 · Answer

Well we know parallel lines have the same slope...so we can start with that..

y = 3x + 2

This is slope intercept form   y = mx + b    where 'm' is the slope of the line...

So there....'m' = 3 so the slope is 3...just like the line we are looking for...

We need our line to pass through (5 , -6) (x , y)
We can plug in the 'm' we have...and also the point we have into the point slope formula

$$\large y - y_0 = m(x - x_0)$$

After plugging in we have

$$\large y + 6 = 3(x - 5)$$
$$\large y = 3x - 21$$

This would be our line...and to put this in standard form we just subtract the 3x from both sides to get this to look like

$$\large Ax + By = C$$

$$\large -3x + y = -21$$

and that is our line

anonymous · Answer

one more question. :/ sorry guys!!

solve f(x)=x^2-4x+3 for f(-2)

anonymous · Answer

and thank you sooooo much!!! :D

johnweldon1993 · Answer

if 

$$\large f(x) = x^2 - 4x + 3$$
f(-2) would be that same equation...except wherever you see an 'x' you replace it with (-2)

so

$$\large f(-2) = (-2)^2 - 4(-2) + 3$$
$$\large f(-2) = 4 - (-8) + 3$$
$$\large f(-2) = 4 + 8 + 3 = \space ?$$

anonymous · Answer

eehhmmmmm? 0.o need I say that im LITERALLY brain dead with math.. :/ sorry.

johnweldon1993 · Answer

Lol don't worry about it :)

Alright so lets start over

$$\large f(x) = x^2 - 4x + 3$$

this is our original equation right?

johnweldon1993 · Answer

And we need to find 

$$\large f(-2)$$

johnweldon1993 · Answer

See how it went from

$$\large f(x) \rightarrow f(-2)$$
the only thing that changed...is where 'x' once was...it is now -2
So in order to solve our equation...that's all WE need to do too...replace every 'x' we see in the equation...and replace it with -2

johnweldon1993 · Answer

$$\large f(x) = x^2 - 4x + 3$$
now becomes
$$\large f(-2) = (-2)^2 - 4(-2) + 3$$
All that happened was I replaced $\large x^2$ with $\large (-2)^2$ and $\large -4x$ with $\large -4(-2)$

johnweldon1993 · Answer

So now we have

$$\large f(-2) = (-2)^2 - 4(-2) + 3$$
$$\large f(-2) = 4 - (-8) + 3$$
$$\large f(-2) = 4 + 8 + 3$$
$$\large f(-2) = 15$$

anonymous · Answer

omg thats alot easier after you break it up. :3 thank you!!

anonymous · Answer

what processes are needed to solve for functions and thier inverses?

anonymous · Answer

needs to be done in under a min >.<

johnweldon1993 · Answer

To solve for a functions inverse...you need to 

1) switch the 'x' and the 'y' in the original function
2) solve for 'y' again