Lines and simultaneous equations

[moeysquids]

For what value(s) of k (if any) will the line 2x + ky = 3k satisfy the stated condition:
(a) have slope 3?
(b) have y-intercept 3?
(c) pass through (1, 2) ?

Need to show working out. please help

 

[Harry_the_cat]

Can you rearrange the equation into the form y = ... ?

 

[moeysquids]

Yes I'm sure you can. Based off some of the examples the lecturer posted. I need to present how to solve this tomorrow and I'm really stuck.

 

[Deleted member 4993]

Yes I'm sure you can. Based off some of the examples the lecturer posted. I need to present how to solve this tomorrow and I'm really stuck.

You need to tell us exactly where did you get stuck - so that we know where to begin to help you !

What is the equation of a straight line?

What is the definition of the slope of the line? Where in the equation of line (above) it is being used?

What is the definition of the y-intercept of the line? Where in the equation of line (above) it is being used?

 

[moeysquids]

I honestly need help from the very beginning. Here's some notes, hopefully it helps

 

[moeysquids]

.

 

[Harry_the_cat]

Yes I'm sure you can. Based off some of the examples the lecturer posted. I need to present how to solve this tomorrow and I'm really stuck.

So what is the equation in the form y=.... ?

 

[moeysquids]

y = m x + c ?

 

[HallsofIvy]

That was not the question! You have an equation of the form 2x + ky = 3k.
Yes, such an equation can be put into the form "y= mx+ c" for some numbers m and c. The question is "what are m and c for this particular equation. You need to solve that equation for y.

Subtract 2x from both sides of the equation to get ky= -2x+ 3k.
Divide both sides of the equation by k to get y= (-2/k)x+ 3.

NOW, what are the slope and the x and y intercepts?

 

[moeysquids]

I think the question is telling us to solve K for each of those conditions.

I'm very confused. Maths is my weakness

 

[HallsofIvy]

Yes. the problem said

For what value(s) of k (if any) will the line 2x + ky = 3k satisfy the stated condition:
(a) have slope 3?
(b) have y-intercept 3?
(c) pass through (1, 2) ?

Need to show working out. please help

You have been told that you can write that equation as \(\displaystyle y= -\frac{2}{k}+ 3\), that the slope 3 is \(\displaystyle -\frac{2}{k}\) and that the y-intercept is 3.

a) have slope 3: Solve \(\displaystyle -\frac{2}{k}= 2\).
b) have y- intercept 3: That is true for all k.
c) pass through (1, 2): When 2(1)+ k(2)= 3k. Solve that for k.

 

[moeysquids]

Yeah makes sense. I have to show how I achieved those results in my presentation

 

[lex]

For what value(s) of k (if any) will the line 2x + ky = 3k satisfy the stated condition:
(a) have slope 3?
(b) have y-intercept 3?
(c) pass through (1, 2) ?

b) have y- intercept 3: That is true for all k.

A minor amendment:
(b) is true for all k≠0

When k=0, 2x + ky = 3k becomes x=0, which is a vertical line (the y-axis). It wouldn't be appropriate to say the y-intercept is 3.
The form [MATH]y=-\frac{2}{k}x+3[/MATH] only applies when k≠0. When k=0 we must use the original form 2x + ky = 3k

a) have slope 3: Solve [MATH]-\frac{2}{k}= 2[/MATH].

Also (a) Solve [MATH]-\frac{2}{k}= 3[/MATH]