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Equations - I think I've gone wrong - but Im not sure.

The equations of the lines are given below -
Line A y=2x+3
Line B y= 1/2x-3
Line C y=6-x
Line D y-2x=7 Rearranged = y=2x+7
Line E y+2x=3 Rearranged = y=-2x+3

If I use x=1
A- Y=5
B- Y=-2.5
C- Y=5
D- Y=9
E- Y=1

(a) which line goes through the point (1,9) - (D)
(B)which two lines cross the y axis at the same point - For this I would say A&C However, the question is multi choice and A&C are not an answer.
(C) which two lines are parallel - A&D
(D) which two lines are perpendicular- B&E

Could someone explain where I've gone wrong?

(edited 3 years ago)

Anyone able to help?

Original post by noodlestopshop

Anyone able to help?

Yes - it would help to rewrite all in the form y = mx + c

Only part (a) is correct.

For (c) you want the two lines with same value of c.

Reply 3

username5352678

Original post by noodlestopshop

Anyone able to help?

check which of your equations has the same c value (i.e number added/subtracted to the x value)

Reply 4

boulderingislife

Original post by noodlestopshop

The equations of the lines are given below -
Line A y=2x+3
Line B y= 1/2x-3
Line C y=6-x
Line D y-2x=7 Rearranged = y=7+2x
Line E y+2x=3 Rearranged = y=3-2x

If I use x=1
A- Y=5
B- Y=-2.5
C- Y=5
D- Y=9
E- Y=1

(a) which line goes through the point (1,9) - (D)
(B)which two lines cross the y axis at the same point - For this I would say A&C However, the question is multi choice and A&C are not an answer. Crosses y axis at x = 0. You will see for A this gives 3 and for C, 6.
(C) which two lines are parallel - D&E (A and d) - parallel means number in front of x is same, ie 2 in this case.
(D) which two lines are perpendicular- I tried multiplying gradients but can't find one which gives -1. (B and e)

Could someone explain where I've gone wrong?

See commented above. Also for the gradient one I think it is b and e only if b is: (1/2)*(x-3). If the x is on the bottom then i’m at a loss like you! Put brackets as appropriate in the Etqn for B

(edited 3 years ago)

Reply 5

username5352678

Original post by Muttley79

Yes - it would help to rewrite all in the form y = mx + c

Only part (a) is correct.

For (c) you want the two lines with same value of c.

for c) don't you want to gradients that multiply to make -1?

Reply 6

username5380844

Original post by Muttley79

Yes - it would help to rewrite all in the form y = mx + c

Only part (a) is correct.

For (c) you want the two lines with same value of c.

which are not in the form y = mx + c ?

Reply 7

username5352678

Original post by noodlestopshop

which are not in the form y = mx + c ?

I think they mean rearrange the last two equations

Reply 8

username5380844

Original post by Medi-cry

I think they mean rearrange the last two equations

didn't I do that already tho or is there something wrong with mine?

Reply 9

mzmthe1

do you want an answer because I can give you it? ill give you the explanation first... answer a is the only correct one. question b reuqires you to chnage all equations to y=mx c. the reason why a and c are not an option is that when x is 0 the y value is not the same. Line A would have a y intercept of 6 and Line B would have a y-intercept of 3. to make myself clear, for this question you are looking for y intercept (c) values that are equal. with question d, i don't think you have tried all combos. overall, looking through this with more time will help. also, if you want a quick check, then chuck the functions on desmos. hope this helps and I made myself clear.