Can Someone Please help me with this math HW? math wizes and geniouses!!!!?

Question

i checked in the back of the book and it said x=-2

the question says:
write in slope intercept form the equation of the line passing through the given point and perpendicular to the given line.

so it give
(-2,2), y=7
so i sub in 2 for y1 and -2 for x1,
the opposite reciprocal is -1/7
y-2=-1/7(x--2)
or
y-2=-1/7(x+2)
so i distributed
-1/7(x)= -1/7x and -1/7(2)=-2/7
y-2=-1/7x-2/7
then i added 2 to both sides leaving
y=-1/7x-2/7
and the answer in the back is x= -2
what did i do wrong

Answer 1

perpendicular to y=7
so slope=1/0
passing through (-2,2)
equation y-2=1/0(x+2)
0(y-2)=x+2
so x=-2 is the required equation

Answer 2

So you want to find the equation of the line perpendicular to the line y = 7, through the point (-2, 2). As a side note, y = 7 is a horizontal line, and can be rewritten y = 0x + 7. That means the slope is 0.

Now, what is the opposite reciprocal? There is none! You can't take the reciprocal of 0 (since 1/0 is undefined). Your conclusion is that since y = 7 is a horizontal line, the equation of your line perpendicular to y = 7 should be a vertical line.

What vertical line passes through the point (-2, 2)? The obvious answer to that is x = -2 (just look at the x-coordinate).

Therefore, the equation of your line is x = -2.

Recall that the slope of a line is given by the formula
m = (y2 - y1) / (x2 - x1)

If you substitute 2 for y1 and -2 for x1, you would get

m = (y2 - 2) / (x2 - (-2))

What did you plug in for x2 and y2? A slope requires two points. That's where you went wrong.

Answer 3

The line y=7 is a horizontal line (that does not pass through the point (-2,2)). It can also be written as y = 0x + 7, which shows you that the slope of the line is zero. You will notice that in seeking the negative reciprocal of zero you have to divide by zero (which is not possible). Instead we know that a verticle line is perpendicular to a horizontal line. The formula of a vericle line, passing through a that point (where x= -2) is x= -2.

So what you got confused was that you saw the intercept and thought it was the slope.

It's funny because you can't write this line in slope intercept form, since y is infinite, also noted by the fact that the answer in the back of the book is not in slope intercept form...

Answer 4

Y = 7 is a horizontal line, so it's gradient (slope) is 0.

The line perpendicular to that will have an undefined (infinite) gradient because it will be a vertical line.

Because of this the line will be written in the form x = ...

Since you are given the point (-2,2), the x co'ordinate is the one you must use.

So the line will be x = -2

Answer 5

the slope is not 7: the equation y = 7 indicates a horizontal line (slope of 0)
a line perpendicular to this one would have infinite slope because it is a vertical line. the equation is x = -2 because the vertical line rises straight up from (-2, 2) and because it is vertical, the x value doesn't change

Answer 6

you purchased it! commonly in severe college algebra by technique of opposite we propose additive inverse and by technique of reciprocal we propose multiplicative inverse. So if it is what you propose, to get the alternative you alter the sign, and to get the reciprocal you turn it over. so which you purchased it suited, the alternative reciprocal of 7 is -a million/7. in case you have a line with slope 7, a line with slope -a million/7 may be perpendicular to that line.

Answer 7

well one thing is that you ended uo with y-2=1/7x-2/7,
you need to isolate the y and add 2 to each side.