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Could someone show me and explain what the general form equation of the points (-7,2) and (1,6) is?

2007-08-12 09:23:06 · 5 answers · asked by Jake P 2 in Science & Mathematics Mathematics

5 answers

slope formula

m = y₂- y₁/ x₂- x₁

Ordered Pairs

(- 7, 2)(1, 6)

m = 6 - 2 / 1 - ( - 7)

m = 4 / 1 + 8

m = 4 / 8

m = 1/2

- - - - - - - - -

Slope intercept form

y = mx + b

Ordered Pair

(- 7, 2)

2 = 1/2(- 7) + b

2 = - 7/2 + b

Transpose 7/2

2 + 7/2 = - 7/2 + b + 7/2

4/2 + 7/2 = b

Add the numerator

11/2 = b

- - - - - - -

The equation

y = 1/2x + 11/2

Multiply both sides of the eqution by 2

2y = 2(1/2x) + 2(11/2)

2y = x + 11

Transpose x

- x + 2y = x + 11 - x

- x + 2y = 11

Transpose 11

- x + 2y - 11= 11 - 11

- x + 2y - 11 = 0

- - - - - - - - -s-

2007-08-12 10:34:48 · answer #1 · answered by SAMUEL D 7 · 0 0

Tou have only two points, therefore the equation will represent a straight line.

The "standard" form (or general form) of the equation is:
y = mx + c

where m is the "slope" (by how much does y increase when x increases by 1?) and c is the "intercept" (where does the line cross the y axis?).

The slope can be found by finding the change in y for the corresponding change in x.

Each point is given in the form (x, y).

You have:
(-7, 2) and (1, 6)
It does not matter in what order you do this, as long as you keep the same order for both variables:

x goes from -7 to +1, a change of +8
y goes from +2 to +6, a change of +4

The rate of change of y, in relation to x, is 4/8 = 1/2
Therefore m = 1/2 (or 0.5)

y = 0.5 x + c

We can use the values of the known points for x and y. Let's use (x, y) = (1,6)

6 = 0.5*1 + c
6 = 0.5 + c
6 - 0.5 = c
5.5 = c

y = 0.5 x + 5.5

Let's check with the other point (x, y) = (-7, 2)

2 ?=? 0.5*(-7) + 5.5
2 ?=? -3.5 + 5.5
2 ?=? 2
TRUE

(I wrote ?=? because we were checking if the equality was true; we did not know yet).

2007-08-12 16:35:26 · answer #2 · answered by Raymond 7 · 0 0

Equation of the line thru the points (-7,2) and (1,6)
slope of the line, m = (6 - 2) / ( 1 - (-7))
= 4/8 = 1/2

(y - 6) / (x - 1) = m = 1/2
y - 6 = (1/2)(x - 1)
2(y - 6) = x -1
2y - 12 = x - 1
2y - x - 11 = 0

2007-08-12 16:28:45 · answer #3 · answered by vlee1225 6 · 0 0

i know how u feel im 16 and i hate chem, AND math i suckd at it so bad... thanks god my chem teacher loved , she was awsome...lol but my math teacher failed me!! i had summer school this summer 250dollars!!! i hate her!!!

2007-08-12 16:29:51 · answer #4 · answered by Anonymous · 0 0

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)
(y-2)/(x+7)=(6-2)/(1+7)
(y-2)/(x+7)=4/8=1/2
2y-4=x+7
2y-x=11

2007-08-12 16:29:22 · answer #5 · answered by Anonymous · 0 0

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