## anonymous 5 years ago I am trying to find an equation using the give pair of points (1/4,-1/2) and (3/4,3)

1. anonymous

You need to use the two-point formula for a line. It says, if you have two points,$(x_1,y_1)$and$(x_2,y_2)$then the equation of the line containing those points is$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$You can make any one of your two points be (x1,y1). The other will have to be the (x2,y2). So here, you'd have$y-(-\frac{1}{2})=\frac{3-(-1/2)}{3/4-1}(x-1/4)$that is$y+1/2=\frac{7/2}{-1/4}(x-1/4) \rightarrow y = -14(x-1/4)-1/2$

2. anonymous

You can expand to get$y=-14x+7/2-1/2=-14x+3$So$y=-14x+3$

3. anonymous

we are suppossed to use the mx+b formula is what it says. Is that possible?

4. anonymous

Sure. You should have said so! :) I'll do it differently.

5. anonymous

Well, actually, if you notice when I gave you the two-point formula, outside the $(x-x_1)$part there is$\frac{y_2-y_1}{x_2-x_1}$...that's the slope, m. So you can calculate that first, then you pick any one of the two points to do the rest$y-y_1=m(x-x_1)$

6. anonymous

They're actually the same formula...you get m from the two points.

7. anonymous

You're not actually told the intercept in your question, so can't read off 'b'. You would need to have one of your points, (0,b).

8. anonymous

So, if you were given two points, (1,2) and (0,3), you could use y=mx+b as: m= (3-2)/(0-1)=-1 b=3 so y=-x+3

9. anonymous

Your question's slightly different; you can't jump to y=mx+b...you need to find b from the points like I've done.

10. anonymous

the only points i have are (1/4,-1/2) and (3/4,3) sorry i did not mention it before. At the bottom it says what is the equation of the line? y= (Simplify your answer.Type the answer in the form y=mx+b using intergers or fractions) this is why I am having so much problem trying to figure out what they want me to do because everytime I put in an answer they say it is wrong

11. anonymous

Okay...they're saying "Find the equation of the line ANY way you like (from ways you're taught) and THEN put it in the form y=mx+b...then type that in." I'll do it on paper to double-check.

12. anonymous

okay- I made a mistake before - when I type on the fly, I sometimes stuff up. The equation of your line in the form you need is$y=7x-\frac{9}{4}$

13. anonymous

ok that was right that time. thanks

14. anonymous

np

15. anonymous

ok now I have to write an equation of the line containing the given point and parallel to the given line. express your answer in the form of y=mx+b (6,7);x+7y=2

16. anonymous

Well, the second line needs to be parallel to the first, so it must have the same slope. You should arrange the first equation in the form y=mx+b and then 'read off' the slope. That will be the slope of the second line. Now, since you have a point that the second line must have, and the slope, you can use the point-slope formula I gave above y - y1 = m(x - x1) You expand and rewrite it as a last step in the form you need.

17. anonymous

ok so the slope would be 1 then right?

18. anonymous

No...you have to put the equation in the right form. x+7y=2 is NOT in the form y=mx+_b

19. anonymous

$y=-\frac{1}{7}x+\frac{2}{7}$

20. anonymous

So the slope is -1/7

21. anonymous

Your new line will be$y-y_1=m(x-x_1) \rightarrow y-7=-\frac{1}{7}(x-6)$

22. anonymous

$y=-\frac{1}{7}x+\frac{55}{7}$when you rearrange and put it into the form you need.

23. anonymous

so would I do the same thig with these points (-2.5);5x=7y+8

24. anonymous

What are you being asked to do?