## anonymous one year ago The two lines 3x-y-1=0 and x+3y-5=0 are: a) perpendicular b) parallel c) confounded d) collinear

1. IrishBoy123

you might wish to compare their slopes re-writing each as $$y = ...$$ would help you do that

2. anonymous

i got x=3/5. and y=4/5. but now no idea how to continue

3. anonymous

Is confounded points even a thing?

4. anonymous

the right answer is a- but how to know if 2 lines are perp/paral/conf ?

5. IrishBoy123

what you have done is found *incorrectly* the intersection point. plug your answer back into both equations to see. as i said, if you re-write both equations in $$y = mx + c$$ form, you will see m, ie the slope, for each. we can go from there. [and i know that n some countries they use $$y = ax + b$$ or $$y = mx + b$$ but do that first....]

6. IrishBoy123

@Sepeario i don't think so. i actually looked it up :p

7. anonymous

oki so i got the first y1=3x-1 and y2=(-x/3)-(5/3) what is the next step?

8. IrishBoy123

y2 has an error in it but this is the missing bit of information you need when you multiply the slopes of lines that are perpendicular, you get -1 https://gyazo.com/1fa13ef12ef26796eab06a832615537a

9. anonymous

ohhh thank you so much you were so helpful. A little more question, how to know if they are parallel?

10. phi

FYI, you should get the equations $y = 3x -1 \\y= -\frac{1}{3} x + \frac{5}{3}$ compare the slopes: if they are the same the lines are parallel (unless you have the exact same equation for both, in which case they are the same line) if the slopes are *negative reciprocals*, the lines are perpendicular (form a right angle where they cross) negative reciprocal means "flip" and multiply by -1 for examples: 2/3 and -3/2 (first flip 2/3 to get 3/2 , then negate to get -3/2) or 2 and -1/2 : flip 2 (think of it as 2/1) to get 1/2 , then negate: -1/2 or -1/4 and 4 etc the other test is if you multiply them you get -1 as Irish explained up above