Question

Will medal and fan! Use the point slope form, write an equation for the line perpendicular to the line y = -2(x - 5) containing the point (3,4).

Answer 1

Point slope form: \[y-y _{1}=m(x-x _{1})\]

Answer 2

any ideas on what the slope of \(\bf y = -2(x - 5)\) is?

Answer 3

-2 is the slope right?

Answer 4

@jdoe0001

Answer 5

yep that's right :

Answer 6

So what's the next step?

Answer 7

perpendicular slopes are negative reciprocal
if slope of first equation is a/b then slope of perpendicular line would be negative b/a

Answer 8

So it would be -1/2?

Answer 9

hmm no.

Answer 10

slope is -2/

a perpendicular line to that one, as Nnesha said, would have a NEGATIVE RECIPROCAL SLOPE, or \(\bf slope=-2\qquad negative\implies +2\qquad reciprocal\implies +\cfrac{1}{2}\)

Answer 11

^

Answer 12

Oh positive 1/2! whoops

Answer 13

So once I find that then what?

Answer 14

so, you're really looking for the equation of a line that has a slope of 1/2 and passes through (3,4) \(\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({\color{red}{ 3}}\quad ,&{\color{blue}{ 4}})\quad
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}=\cfrac{1}{2}
\\ \quad \\
% point-slope intercept
y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 15

So that would equal y - 4 = 1/2x - 3/2

Answer 16

y = 1/2x +5/2 would be the answer right?

Answer 17

yeap

Answer 18

That's the answer? Sorry I wasn't sure which reply you were saying yes to.

Answer 19

@jdoe0001

Answer 20

Okay thanks!

Answer 21

even more typos

Answer 22

\(\bf y-4=\cfrac{1}{2}(x-3)\implies y=\cfrac{1}{2}x-\cfrac{3}{2}+4\implies y=\cfrac{1}{2}x-\cfrac{3}{2}+\cfrac{8}{2}
\\ \quad \\y=\cfrac{1}{2}x+\cfrac{5}{2}\)

Answer 23

Lol it's okay. I got it! :)

Answer 24

:)

Answer 25

o^_^o