could someone please help me.

A straight line L has equation y = kx+1 , where k is a constant.

Given that L does not meet or intersect y=|2x+9|+3,

find the range of possible values of k.

Thanks

A straight line L has equation y = kx+1 , where k is a constant.

Given that L does not meet or intersect y=|2x+9|+3,

find the range of possible values of k.

Thanks

(edited 1 year ago)

Per discussion board rules, please do post some of your thoughts/workings.

I'd say there are quite a few ways to do this. It would be helpful if you had a decent attempt (or even just thought, right or wrong), then we go from there. It's all about effort.

I'd say there are quite a few ways to do this. It would be helpful if you had a decent attempt (or even just thought, right or wrong), then we go from there. It's all about effort.

(edited 1 year ago)

Original post by tonyiptony

Per discussion board rules, please do post some of your thoughts/workings.

I'd say there are quite a few ways to do this. It would be helpful if you had a decent attempt (or even just thought, right or wrong), then we go from there. It's all about effort.

I'd say there are quite a few ways to do this. It would be helpful if you had a decent attempt (or even just thought, right or wrong), then we go from there. It's all about effort.

ok so as a starting point im guessing the graph of y=kx+1 touches the y axis at (0,1), the line must touch the x axis at y<3 but im really confused.

Original post by exclusiv360

ok so as a starting point im guessing the graph of y=kx+1 touches the y axis at (0,1), the line must touch the x axis at y<3 but im really confused.

Hmm... not sure how you get to that deduction (or rather I'm not sure what you mean by that).

Also as a remark, this is not an easy problem, so it's alright if you are confused .

Perhaps I'll give you a head start? Two ways from here in spoilers:

(1) Algebraic (not recommended as you'll soon find out, but try regardless):

Spoiler

(2) Geometric (far more elegant way of solving IMO, but I'm not sure how to write the solution out that presents the narrative):

Spoiler

We are at investigation stage right now, so don't rush (or so I hope you don't).

(edited 1 year ago)

Original post by exclusiv360

could someone please help me.

A straight line L has equation y = kx+1 , where k is a constant.

Given that L does not meet or intersect y=|2x+9|+3,

find the range of possible values of k.

Thanks

A straight line L has equation y = kx+1 , where k is a constant.

Given that L does not meet or intersect y=|2x+9|+3,

find the range of possible values of k.

Thanks

well y=|2x+9|+3 has two lines. one is y=2x+12 and the other is y=-2x-6

so equate y=kx+1 to these 2 lines to find the value of k. and whatever k isn't must be your answer

Original post by alberw21

well y=|2x+9|+3 has two lines. one is y=2x+12 and the other is y=-2x-6

so equate y=kx+1 to these 2 lines to find the value of k. and whatever k isn't must be your answer

so equate y=kx+1 to these 2 lines to find the value of k. and whatever k isn't must be your answer

im getting k=11/x + 2 and k= -7/x - 2 what can this tell me?

i'm also stuck on this one, i'm getting k is inbetween -2 and 2?

Original post by exclusiv360

im getting k=11/x + 2 and k= -7/x - 2 what can this tell me?

Well, it sort of doesn't tell you anything. But there is a key point that alberw was omitting.

When is y=|2x+9|+3 the same as y=2x+12? And when is it the same as y=-2x-6?

That's why I specifically mention under "algebraic method" whether you know [spoilers]:

Spoiler

(Also the algebraic method is full of traps if you aren't careful. You've stepped onto one of many.)

(edited 1 year ago)

Original post by tonyiptony

Well, it sort of doesn't tell you anything. But there is a key point that alberw was omitting.

When is y=|2x+9|+3 the same as y=2x+12? And when is it the same as y=-2x-6?

That's why I specifically mention under "algebraic method" whether you know [spoilers]:

(Also the algebraic method is full of traps if you aren't careful. You've stepped onto one of many.)

When is y=|2x+9|+3 the same as y=2x+12? And when is it the same as y=-2x-6?

That's why I specifically mention under "algebraic method" whether you know [spoilers]:

Spoiler

(Also the algebraic method is full of traps if you aren't careful. You've stepped onto one of many.)

quite confused still

Original post by exclusiv360

quite confused still

Hmm... you might want to reread what I said in #4.

If you aren't sure what I mean in #8, then you probably haven't mastered "solving equations with absolute values/modulus signs".

Though again, don't worry, I said in #4 that there is another way that completely circumvent the issue.

I encourage you to just say what you've discovered, what you think along the way. Could be wrong, could be right, could run into another obstacle - it's all good progress!

(edited 1 year ago)

Original post by exclusiv360

quite confused still

y=|2x+9|+3 is not the same as y=2x+12 because the first equation involves a transformation as shown by the +3

Original post by exclusiv360

quite confused still

Tonys advice about sketching it is the simplest way to do it (is it graphs topic?) and by marking the lowest point for

|2x+9|+3

you can almost write the answer down. Think about what happens when you rotate (vary k) the line about (0,1).

Upload your sketch if you're still unsure, though you can also try checking in desmos.

(edited 1 year ago)

Original post by exclusiv360

im getting k=11/x + 2 and k= -7/x - 2 what can this tell me?

you can solve them simultaneously to find k and x

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