Coordinate Algebra and Geometry?

Question

i have some problems to begin my school year with that i was supposed to learn last year, but my teacher never taught me or i have no idea how to do it. Please help. 

1) Write the equation in point slope form, y-y1 = m (x-x1), for each given line: line through (2,1) and (-1, -8)

2) (Is the same as one, but it gives me a slope and a point. What is point slope form anyway?)

Also, the third question says to 'list 3 points on the line for each given line' and gives me 2x + y = 9. I know how to find the x and y intercept and get the ordered pairs, but how do i find other points of a line without graphing it? For example, if i had (0, -2) and (-2, 0), how would i find another point on that line without graphing it? I think that's what the question is asking...

Please help me with this, and please try to be through and simple. Thank you in advance.

Philo · Accepted Answer

1) slope of the line
∙ ∙ change in y, 1 → -8, is -9
∙ ∙ change in x, 2 → -1, is -3 ∙ ∙ ∙ so slope is -9/-3 = 3
∙ ∙ using (2,1) as the point (x1, y1) the equation is
∙ ∙ y – 1 = 3(x – 2)
∙ ∙ that's point-slope form.

2) if you have the slope you don't need a 2nd point to find it, just fill in the form as above.

3) pick an x, compute the y.  intercepts are easy since one of your picks is 0.
∙ ∙ so for 2x + y = 9, when 
∙ ∙ x = 0, y = 9 ∙ ∙ ∙ and when
∙ ∙ x = 1, y = 7

notice slope is -2, so when x goes up 1, y goes down 2.  should make plotting points easy.

Castigator · Answer

well i'll work the first one for you

m = -9/-3 = 3

y-1 = 3 (x-2)

y = 3x - 5

m is the gradient or slope and you find it by (-8-1) / (-1-2) = y2 - y1 / x2 - x1

point slope form is:y=mx+c

or for example:y=3x - 5

use the slope = m and the point to construct an equation using y - y1 =m (x-x1) and you will be good

Yeah just use those 2 intercepts and try graphing it should be correct since your intercepts seem to be right.

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Coordinate Algebra and Geometry?

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