What is the slope to this question?!?

Question

Find the value of y so that the line through (-2,-1) and (10,y) is perpendicular to the line through (6,-2) and (5,7).

I don't want the answer, just the explanation on how to do it....Thanks!

Answer 1

first find the slope of  (6,-2) and (5,7). = change in y/ change in x

then as the new line is perpendicular tkae the slope and flip the sign and flip over the fraction.( make the negative reciprocal)

then make thisnew slope equal to  = y- -1/ 10- -2

then find y

Answer 2

ok. start by drawing the lines from the last two coordinates and draw the point of the first coordinate.   with those on a seperate piece of paper do the math on the second coordinates.   6-5=1 and -2-7 you get your slope on that line.   1/9  if a line is perpendicular in must mean that the slope is the exact opposite of the 1/9 line, meaning that the first slope is 9/1 count it out from -2  -1 and you should get your anwser

Answer 3

In order for two lines to be perpendicular to each other, their slopes must be the negative reciprocals of each other....

So..... let's find the slope of the line that runs through points (6, -2) and (5,7)

You find the slope by using the following formula....

Slope of Line1 = m1 = (y2-y1) / (x2-x1)

..... so let (x1,y1) = (6,-2).... and let (x2,y2) = (5,7)

Plugging in the values for x1, y1, x2, and y2.... you get....

m = [ 7 - (-2) ] / (5 - 6) = (7+2) / (5 - 6) = 9 / -1 = - 9/1 = -9

What is the negative reciprocal of -9? The negative reciprocal of m = -9 is - 1/m = -1 / (-9) = +1/9 = 1/9

So the slope of Line 2 to be perpendicular to Line 1.... must have a slope of 1/9

Slope of Line 2 = m2 = [ y - (-1) ] / [ 10 - (-2) ]

m2 = (y+1) / (10+2) = (y+1) / 12

.......... (y+1) ......... 1

m2 = -------------- = -------- <== because m2 = -1 / m1 = -1 / (-9) = +1/9

............. 12 .......... 9

Cross multiplying.... you get.....

(y+1)(9) = (12)(1)

Distribute the "9" to both the "y" and the "+1".... like this...

(y)(9) + (+1)(9) = 12

9y + 9 = 12

Subtract "9" from both sides like this...

9y + 9 = 12

..... - 9 ... -9

---------------------

9y + 0 = 3

9y = 3

Divide both sides by "9"... like this...

9y ... 3

---- = ----

9 ..... 9

The 9's on the left side cancel each other out... leaving you with.... y = 3/9 = 1/3.....

So when " y = 1/3 ".... the line that runs through the first set of points.... will be perpendicular to the line that runs through the 2nd set of points.....