Question

Give the slope-intercept form of the equation of the line that is perpendicular to and contains (-1, 9).

I know the slope intercept form is y=mx+b  I also know that perpendicular lines have negative reciprocals of each other. I just don't know what to do now.

Answer 1

Start by solving for y to get this in y=mx+b form

subtract 5x from both sides

4y=-5x+4

divide by 4

y=4/5x+4/4

simplify to

y=4/5x+1

Now you know that the slope of the first line is 4/5

The slope of the second line is -4/5

so the second equation is

y=-4/5x+?

since the line has to cross the point -1,9 you can plot that point on the graph and then use the slope to find another point.

from the point -1,9 you can use rise over run to go down the graph 4 spots to 5 and to the right on the graph 5 spots to 4

your second point would be (4,5)

y=-4/5x+41/5 is the equation for the second line

connect those points to get your line.  The two lines look like this:

Answer 2

5x + 4y= 4

isolate the y to one side

4y= -5x+4

divide by 4 on both sides

y= -5/4x +1 

the slope is -5/4x, and the perpendicular line would be 4/5x (reciprocal)

for (-1,9), plug the -1 for x, that would give you y into the equation in bold.

then plug the 9 in for y, and that would give you the x in the equation in bold.