March 15, 2007

HELLO! =)

the things we did today:
1. we checked whether anyone's having a hard time answering any number in exercise 14.
2. ms. armstrong told us that the analytic geometry test will be on monday, not tomorrow. tomorrow will be our work period.
3. ms. armstrong taught us how to determine the equations of lines; standard form or slope-intercept form.


First of all, standard form looks like this, Ax + By + C = 0. So if you see an equation that's in this format, it is in standard form. always remember that a, b, and c are integers. they can never be fractions. Then, slope-intercept form looks like this, y = mx + b. It is okay if you have m or b as fractions.

Now that you know that, you can now find the standard form or slope-intercept form even if the only information given are the 2 points.

for example:
Find the standard form of the equation of a line containing (6,1) and (-4,3)

first you ask yourself, what are you asked to find? in this equation, you are asked to find for the standard form of the equation. (Ax + By + C = 0)

second, what info are you given? the 2 points : (6,1) and (-4,3)

third, how can you use that info? since you have 2 points, you can try finding the slope.

m = y² - y1 / x2 - x1
m = 3-1 / -4-3
m = 2 /-1
m = -1/5

now, that you've find out the slope, what equation can you use using a slope and a point?
POINT-SLOPE EQUATION. slope = -1/5 , points = (6,1) or (-4,3) - just chose between the 2 points. and then just substitute these numbers into the formula.

(y-y¹) = m(x-x¹) - formula of point-slope equation
y-1 = -1/5 (x-6)
--in this part, the first thing that comes into your mind is to just multiply -1/5 to x-6. But if you do that you'll have a fraction and remember, you can't have a fraction in a standard form. So what you do is, just multiply 5 to both sides so that you can eliminate the fraction -1/5
5(y-1) = (-1/5 (x-6) )5
5y-5 = -x+6
x+5y-5-6 = 0
x+5y-11 = 0 - i transfered everything to the other side because remember the standard
form should look like this (Ax + By + C = 0). Also, always remember that
the x should be always positive. so if the x becomes negative, just transfer
it to the other side along with the other numbers.

the answer is x + 5y - 11 = 0.

So what if you're asked to find for the slope-intercept form and you're given 2 points? you just have to do the same steps. find for the slope and do the point-slope equation. and you can determine the equation of the line already.


I think that's it. Also, don't forget to do Exercises 15, and 16.

I really hope i have helped you in some way!

the next one blogging is..(drumroll please)....JENNY! =)

Labels: analytic geometry, janelle, scribe