anonymous one year ago 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).

1. anonymous

Point slope form: $y-y _{1}=m(x-x _{1})$

2. anonymous

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

3. anonymous

-2 is the slope right?

4. anonymous

@jdoe0001

5. Nnesha

yep that's right :

6. anonymous

So what's the next step?

7. Nnesha

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

8. anonymous

So it would be -1/2?

9. Nnesha

hmm no.

10. anonymous

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

11. Nnesha

^

12. anonymous

Oh positive 1/2! whoops

13. anonymous

So once I find that then what?

14. anonymous

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

15. anonymous

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

16. anonymous

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

17. anonymous

yeap

18. anonymous

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

19. anonymous

@jdoe0001

20. anonymous

Okay thanks!

21. anonymous

even more typos

22. anonymous

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

23. anonymous

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

24. anonymous

:)

25. Nnesha

o^_^o