Help please?

Which equation represents the line passing through the point (4, −16) and is perpendicular to the line y equals negative two thirds x plus 8?

Question

Help please?

Which equation represents the line passing through the point (4, −16) and is perpendicular to the line y equals negative two thirds x plus 8?

amistre64 · Answer

where are you stuck at?

anonymous · Answer

How do I draw a line when I only have one point? There's probably a way but I'm not sure how

amistre64 · Answer

you are given a point and a 'slope'.  the slope is just hidden at the moment in the information

anonymous · Answer

Well perpendicular means they cross at a right angle right?

amistre64 · Answer

perpendicular lines have the property that their slopes are negative reciprocals of one another:

if slope1 = 4/5  then the perp slope is -5/4

amistre64 · Answer

yes, they cross at right angles

anonymous · Answer

So I should graph the line they give me first I guess

amistre64 · Answer

you are given a line with a slope of -2/3  and want to apply the perp slope to your solution.  what is the perp slope of -2/3?

anonymous · Answer

3/2?

amistre64 · Answer

yes

now, the line they ask for has a slope of:  3/2

and passes thru the point:  (4,-16)

we have all the information now to make the line equation.

anonymous · Answer

y = 3/2x... how do I find out what comes after that

amistre64 · Answer

well, since we have a point and a slope;  we could very well use what is called the point slope form of a line and then work it to whatever format they have as an option:

given a point (a,b), and a slope, m
              ^^^^                      ^^^^

point slope form is just:  y-b = m(x-a)

which we can rework as:  y = mx - ma + b  if need be to get it into slope intercept form

anonymous · Answer

Well the answers are

a. y = 2/3x - 22
b. y = -2/3x - 22
c. y = -3/2x - 22
d. y = 3/2x - 22

amistre64 · Answer

then it looks like d is our most reasonable choice.

anonymous · Answer

I don't understand where they got the -22 from though

amistre64 · Answer

-3(4)/2 - 16 = 22

amistre64 · Answer

.. = -22

anonymous · Answer

Ooh I understand thank you!!

amistre64 · Answer

$$y-(-16)=\frac 32(x-(4))$$
$$y=\frac 32x-(4)\frac{3}{2}-16$$
$$y=\frac 32x-6-16$$
...

amistre64 · Answer

but since all the options end in -22, that part doesnt really matter to us, the 3/2 slope is the key to simply picking out the right option without all the hulla-ballou

anonymous · Answer

Yeah! thank you for your help

anonymous · Answer

option C....