Question

line that is perpendicular to -x+y=7 and passes through (-1,-1)

Answer 1

First you have to find the slope of the line: -x + y = 7. The easiest way to do that is to change it to slope-intercept form. Can you do that?

Answer 2

what is the eqution of the line

Answer 3

do yo mean like y=mx+b

Answer 4

I got y=-x-7

Answer 5

Exactly, so what's the slope of THAT line?

Answer 6

-1

Answer 7

Perfect. To be technical, let's say \[-\frac{ 1 }{ 1 }\]
Now, do you know what you have to do to the slope of a line in order to get the slope of its perpendicular line? Two things...

Answer 8

change to a positive and keep the y intercept?

Answer 9

no right?

Answer 10

Perpendicular lines have "opposite" and "reciprocal" slopes. So yes, it changes to a positive. And since it's 1/1, the reciprocal is still 1/1 (flipped). So the slope of the perpendicular line is positive 1.
But to find the exact equation that passes through the point (-1, -1) with a slope of 1 (which we just determined), you have to use the point-slope formula. Do you know that?
We can't just keep the old y-intercept.

Answer 11

I don't remember point slope formula is it x2-x1 over y2-y1?

Answer 12

No, that's almost the formula for slope (except the y's are on top).
Point slope is this:
\[y-y _{1}=m(x-x _{1})\]
where \[(x _{1},y _{1})\] is a point on the line, and m is the slope.

Can you plug in what you know? The regular x and y will stay x and y. Just replace the x1, y1, and m. Then we'll simplify.