Verified answer

... 3x - y = 9 ← put equation into the slope-intercept form → y = 3x + 9

In the equation: y = mx + b; m = slope; here the slope = 3

All lines which are paralled to this line will have the same slope;

or will be in the form: y = 3x + b

All lines which are perpendicular to this line will have a negative inverse slope;

or will be in the form: y = -⅓ x + b

there are two ways

1. y = mx +b here m is a slope

so 3x-y=9 is

=> y = 3x-9 so the slope is 3 and the slope of the perpendicular to this line is -1/3

Method 2

ax+by+c = 0 and slope is m = -a/b

so 3x-y =9 is => 3x-y-9= 0 and m = -3/-1 = 3 and slope perpendicular to this line is -1/3

convert it to y=mx + b form. y=3x - 9. parallel lines have the same slope but a different y-intercept. simply replace the "-9" with another number. You can say:

y=3x - 5

a line perpendicular to this would have a slope of "-1/3." so, it would be:

y=-1/3x -9

3x-y=9

-3x -3x

-y=-3x+9

y=3x-9

the slop is 3

the y-intersept is -9

a line perpendicular to this would have a slop of -1/3

and a line parallel to this would have a slop of 3

hope this helps