## anonymous 3 years ago passing through (4,-2) and perpendicular to x=5/4y-2. Write in slope intercept form.

1. anonymous

@zepdrix

2. zepdrix

is the negative 2 also in the denominator? It's a little hard to read correctly without brackets.$\large x=\frac{5}{4y-2}$

3. zepdrix

$\large x=\frac{5}{4}y-2$Oh like this? :) That would make more sense lol

4. anonymous

no it isn't. it's like the second one you just put up.

5. zepdrix

Let's first get our line into slope-intercept form, so we can accurately identify the slope. We want it in this form,$\large y=mx+b$ $\large x=\frac{5}{4}y-2$Start by adding 2 to each side,$\large x+2=\frac{5}{4}y$Multiply each side by 4/5,$\large \frac{4}{5}(x+2)=\left(\frac{5}{4}y\right)\frac{4}{5}$The fractions will cancel out on the right, giving us,$\large y=\frac{4}{5}x+\frac{8}{5}$ So we've got our line in slope-intercept form, this will make it easier to work with. Understand those steps so far?

6. anonymous

oh i had put a -4/5

7. anonymous

but yes other than that i get it so far

8. zepdrix

So it looks like our slope $$\large m$$ is $$\large \dfrac{4}{5}$$. Do you know what it means for a line to be perpendicular? It relates to the slope. :) Since the line we're trying to form is perpendicular to this line, it will have a slope that is a negative reciprocal of this slope. Do you understand what that means? c:

9. anonymous

-4/5 correct? that would be the reciprocal

10. zepdrix

Hmm I believe it's going to be, -5/4. Yes the negative looks good. But then we take the reciprocal (the flip) of our fraction.

11. anonymous

oh okay

12. zepdrix

So we're trying to form an equation for a line perpendicular to the given line. Let's call this new line something likeeeee $$\large y_p$$. So we're trying to get an equation for this line, $$\large y_p=mx+b$$. We've determined that the slope is, $$\large m=-\dfrac{5}{4}$$. Now we need to find the $$\large b$$ value, the y-intercept. To do so, we'll plug in the coordinate pair they gave us, that this line passes through.

13. zepdrix

So plug $$\large (4,-2)$$ into our equation $$\large y_p=-\dfrac{5}{4}x+b$$.

14. anonymous

okay

15. anonymous

i think im messing up so where

16. anonymous

for som reason im getting y=-4/5x+6/5

17. anonymous

i mean -5/4x+6/5

18. zepdrix

So plugging in our point gives us,$\large -2=-\frac{5}{4}(4)+b$The 4's will cancel out,$\large -2=-\frac{5}{\cancel4}(\cancel4)+b$Giving us,$\large -2=-5+b$Adding 5 to each side,$\large b=3$ Did you do something different?

19. anonymous

yeah i did

20. anonymous

i was doing it wrong

21. anonymous

so y=4/5x+8/5 is correct?

22. zepdrix

This was the equation of the line we started with, $\large y=\frac{4}{5}x+\frac{8}{5}$ They gave us a bunch of information to find a different line. And that was this line,$\large y_p=mx+b$ We determined that the slope is $$\large m=-\dfrac{5}{4}$$. And that the y-intercept is $$\large b=3$$.

23. zepdrix

The p doesn't mean anything, you don't need to put that if you don't want. It was just so we could tell it apart from our original y, which referred to a different line.

24. anonymous

25. zepdrix

ya :)

Find more explanations on OpenStudy