1 Pre calculus question, need some help. 10points 2 best answer!!
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1 Pre calculus question, need some help. 10points 2 best answer!!

[From: ] [author: ] [Date: 11-08-15] [Hit: ]
and justify your answer.*If the points (10, -3) and (2,-9) lie on the same line, then the point (-12, -37/2) also lies on that line.......
I got all of the questions on my homework except 4 this one, i need some help please.

Directons: True or False? determine whether the statement is true or false. and justify your answer.

*If the points (10, -3) and (2,-9) lie on the same line, then the point (-12, -37/2) also lies on that line.

So i need some help please, thanks in advance, 10POINTS 4 BEST ANSWER! :)

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Note: All numbers directly after a variable here should actually be subscripts.

Step 1: Find the slope

Slope = m = (y2 - y1)/(x2 - x1) = (-9 + 3)/(2 - 10) = (-6)/(-8) = 3/4

Step 2: Find the equation of the line using the point slope equation for a line

y - y1 = m(x - x1)
y + 3 = (3/4)*(x - 10)
y + 3 = (3/4)*x - 15/2
y = (3/4)*x - 21/2

Step 3: Plug in the x and y values for the point we want to test into our line and see if what we get returns true (if we get like 0 = 1, it's not true... If we get some statement that is true, it's true!)

y = (3/4)*x - 21/2
(-37/2) = (3/4)*(-12) - 21/2
(-37/2) = -9 - 21/2
-37/2 = -39/2

And, just to make it even more obvious, we can multiply both sides by -2...
37 = 39

Definitely false!
The point (-12, -37/2) doesn't lie on the line.

Hope this helps.

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start with the equation of the line. y=mx+b. first find m, the slope. (y1-y2)/(x1-x2) so (-3- -9)/(10-2) = 6/8 or 3/4. now we need to find the y intercept or b. now use either of the two points in your equation. lets use 10, -3 as our point and plug in those as x and y and solve for b. -3=(3/4)(10)+b. solving for b, b = -21/2. now to see if the point they give is on the line, lets plug in -12 for x and see what y is. if we get -37/2, the answer is true. otherwise, false.
y=(3/4)(-12)-(21/2). y = -9 - 21/2 or -39/2 so the answer is false.

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The slope of the line is going to be the "y" distance between the points, divided by the "x" distance between the points.
So, the slope a = (-3+9)/(10-2) = 6/8 = 3/4

The line has an equation of y = ax+b
We know that a is 3/4, so -9 = (3/4)*2 + b, or that b is -10.5

So the equation of the line is y = (3/4)x + 21/10

Does this work with (-12, -37/2)?
(3/4)*(-12) - (10.5) = -39/2

NO, it's false.

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Plug it into your graphing calculator on y= and look at the table. Boom.
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