Question

Find the equation of a line that passes through the point (4,2) that is perpendicular to the line y = x. Show your work. Please help!

Answer 1

what is the slope of \(y=x\) ?

Answer 2

Oh sorry it's y=4/3 x

Answer 3

ok fine
what is the slope of \(y=\frac{4}{3}x\) ?

Answer 4

What do you mean?

Answer 5

Isn't it 4/3?

Answer 6

what do you mean "what do you mean"
in order to answer the question you need the slope of the perpendicular line
in order to find that, you need the slope of the original line


yes it is

Answer 7

Okay so what's the next step?

Answer 8

so the perpendicular line will have a slope that is the "negative reciprocal" which in this case is
\[m=-\frac{3}{4}\]

Answer 9

then since the point is \((4,2)\) and the slope is \(-\frac{3}{4}\) the point slope formula
\[y-y_1=m(x-x_1)\] gives the equation of your line as
\[y-2=-\frac{3}{4}(x-4)\]

Answer 10

I got y=-3x+20

Answer 11

@satellite73

Answer 12

??

Answer 13

seems unlikely
where did the fraction go?

Answer 14

\[y-2=-\frac{3}{4}(x-4)\\
y-2=-\frac{3}{4}x+3\\
y=-\frac{3}{4}x+5\]

Answer 15

you can't get rid of the fraction by multiplying one side by \(4\) without also multiplying the other side by \(4\)