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You need the form y = mx+b. So manipulate the equation to isolate Y.
and m would then be my answer>
Yes, you are looking for m.
practically , - x's coefficient / y's coefficient so , -2/3
So I would first subtract the 2x to the other side, leaving 3y = -2x +6.
Then you divide by 3 since 3y/3 would just leave you with y.
divide both sides by 3 that is.
ok. so if someone asks write the equation of the line through(2 -3) and parallel to y= 4x -1 how would i do thta
Ok you know that the point (2,-3) is going to be on the line of your answer. If two lines are parallel, that means they have the same slope.
So you would substitute your points in, giving you -3 = 4*2 + b
So you have -3 = 8+b. What value of b do you need to make -3 = 8?
Be careful. You need -11.
So since -11 is your b value, you construct your equation. y = 4x - 11. You know that it's 4x because if two lines are parallel they have the same slope. We did those calculations to determine your b value.
so it goes back to the original y- 4x-1?
No. Your answer would be y = 4x -11. This line is parallel to y = 4x -1 because they share the same slope.
the -3= 8 +b is used to find the parallel slope that i need
No, the -3 = 8 +b is used to determine your b value (Your y-intercept)
Two lines are parallel if they share the same slope. that's why you already know your slope for the problem because your answer has to have the same slope as your original line.
can we do one more with different points?
Sure. Do you have an example?
(2 -5) parallel to y=2x+3
Ok. Looking at y = 2x +3, What is the slope of our ansewr going to be?
since they must be parallel
should be 2?
Correct. So for our answer equation right now we have y = 2x + b. Now we must find out b value, and since we are given a point (2,-5), we plug those points into our equation to find our b.
ok so its -5= 2x+b
You forgot to plug in your value for x.
-5 = 2*2 +b
ok. -5=4 +b
Correct. Now what b value do we need to make that equation true?
Correct. Now what's our answer?
this is where i get confused... how do i find this answer
Oh ok. Well the question asks for a line, so we know our answer will be an equation of a line. We need the general form of our answer (meaning leaving x and y as x and y in the answer). We calculated our b value and we know our m value since it has to be parallel to our starting line. y = mx + b. Fill out that equation with the information we calculated (m value and b value).
well slopes the same and b is -9 so its y=2x-9?
so on this everything fallls back to y=mx+b?
Now if you get an answer and your not sure about it, you can just plug in your given point into your answer and if you get the same thing on both sides the equation of your line works with your point.
In this question yes it does. Since your looking for a line your answer will be in the form of y=mx+b
and what if it asks for perpendicular? (1,-1) perpindicular to y=2x+4
Ok a Perpendicular line will have a slope that is the negative reciprocal of the slope of another line. So in this example look at 2 as (2/1). A reciprocal is when you flip the denominator and the numerator, so my reciprocal of 2/1 would be 1/2. Put a negative sign on that and that's the slope of my perpendicular line.
Pops is suited up eh..... that a missionary photo :)
We will calculate our b value the same way as we did before.
Yeah yeah I hear ya lol
ok so -1=2(1) +4
No you plug in your new slope to find the b value. Your new slope would be -1/2
So we would have -1 = -(1/2)*1 + b
so on these you automatically flip the slope
On a perpendicular line yes. And you change the sign.
ok so -1/2 *1 plus b
so then b would be 1/2?
It would be -1/2. You have -1 = -(1/2)*1 + b. -1/2 times 1 is just -1/2. So we're left with -1 = -1/2 + b. b has to be -1/2
two negatives make a positive. so then we plug this back in to y=-1/2x+-1/2?
Two negatives make a positive in multiplication, not addition.
But yes your equation is correct.
And that's your answer.
awesome man i think i got it im having to teach myself this stuff cause i missed days lol
Yeah. If you have a graphing calculator you can understand it better if your a visual learner. I'm more of a hands on / visual type learner myself so it helped me years ago when I was learning this stuff
yea. the only way i learn is to beat it into my head lol. well thanks man can i add you on this site somehow in case i get in a rut?
well you can add me as fan. Idk if it will do anything but I try to get on here some.
ok thanks man