I need help with the following math problem, i don't really even understand what it's asking.?

Question

For each condition below, find all values of k, if any, for which the line 2x+ky= -4k satisfies the condition.
(a) The line has slope 3.
(b) The line has a slope that does not equal 0
(c)The line passes through point (0,4)
(d) The line is horizontal.
(e) The line is vertical


I'm not really looking for the answers, just want to understand what the problem is asking and how to solve.

Answer 1

this is really straight forward.
first get the eq. in the classical y = ax + b format

i'll give you a start in this case it's
1. 2x + ky = -4k

2. 2x + ky (-2x) = -4k (-2x)

3. ky = -4k - 2x

4 ky * (1/k) = (-4k -2x) * (1/k)

5 y = (-4k -2x) *(1/k)

and finally
y = (-2/k)x -4

now answer the question:
a. slope = 3 -> when is (-2/k) equal to 3?
b. slope doesn't equal 0 -> when is (-2/k) not equal to 0
c. if x=0, and y=4, then what's the value of k?
d. horizonal line then slope =0, refer to question a
e. veritcal line then slope = infinite (or is undefined) this is a little tricky , but again refer to question a and ask yourself what' the one number that makes the slope (or the math of it) impossible

good luck

Answer 2

There is an unknown constant "k" in the equation. Each question is asking for a different situation

In (a), they are asking you to find "k", if the slope of the line = 3
To start this, rewrite the equation into slope-intercept form, pretending "k" is a constant:

In slope-intercept form, y = mx + b

2x+ky= -4k
ky = -2x - 4k
y = (-2x - 4k) / k
y = (-2/k)x - 4

So, m = slope = (-2/k) and b = y-intercept = -4
They tell you slope = 3, so set "-2/k" equal to 3 and solve for "k"

-2/k = 3
3k = -2
k = (-2/3)

I'll start you on the others:

(b) The slope does not equal zero, so repeat the above, but set
(-2/k) = 0 Since k is in the denominator, k equals all real numbers, except zero.

(c) If a line passes through a point, (0 , 4), plug those numbers in for (x, y) in "2x+ky= -4k" and solve for "k:

(d) A horizontal line has a "zero" slope, so set slope = 0, and solve for "k"

(e) A vertical line has an "undefined" slope, so when you get an expression for slope here, define "k" based on what it cannot be.

Answer 3

a) The line has slope 3.ky=-2x-4k so y=-2x/k-4 slope -2/k.this is given as 3.so equating -2/k=3 =>k=-2/3
(b) The line has a slope that does not equal 0 slope we found as -2/k -2/k is not 0
(c)The line passes through point (0,4).if the line pases through (0,4) it must satisfy the equation.substituting0+4k=-4k so k=0
(d) The line is horizontal.if the line is horizontal slope=0 and so -2/k=0
(e) The line is vertical if the line is vertical -2/k=1/0 and so k=0

Answer 4

If a function is in the form
y = ax + b, then the slope will be a.
If you don't know what slope means, if a slope is for instance 3, then every unit you advance in the X direction means three units in the Y direction.
Check it out: take function Y = 3x + 2
For x=5, Y must be 17
x=6 -> Y must be 20
x=7 -> y must be 23
You see: for every unit in x, you get three units in y
With this knowledge,
first try to rewrite your function in the form
Y = (something) times X + (something else)
"something" will be the slope.
If you don't know how to rewrite the function check the end.

So what must K be to make something" equal to 3
(queation a), or unequal to zero (b). A horizontal line, doesn't add units in Y when you add units in XX, so the slope is 0. Now, for what values of K is "something" equal to zero? (c)
A vertical line has an infinite slope. Just add a really really small unit to X and Y goes to infinite.
Now for what values of K is "something" infinite.
Hope this helped

Almost forgot: rewriting the function
2X + kY = -4k
so: kY = -2X - 4k
and: Y = (-2X - 4k) / k
= (-2/k) X - 4k/k = (-2/k) X - 4
now what is the slope, or said differently,
if Y = "something" times X + "something else"
what is "something"?

Answer 5

2x+ky=-4k is an equation of a straight line
which you probably better recognize as
y=ax + b (basic formula)

in this basic formula "a" determines the direction (slope) of the line and "b" determines where the line crosses the y-ax (because in that case x=0)

to recognize it easier and make it better to handle you rewrite the equation until it resembles the basic formula. So:

ky = -2x - 4k (deduct both sides 2x)
y = -2x/k - 4k/k (divide both sides by k)
y = -2x/k - 4

Now you should be able to see that the direction/slope of the line is determined by -2/k
and
y = -4 when x = 0

so the line always passes point (0,-4) for every value of "k". But watch out! there is one value k never may get!!!!!!??????

all the other questions deal with the slope of the line
so with the value of -2/k
You probably can find out yourself which values of "k" will be correct in each situation (if not ask for some more tips).
(but again watch out for one value k never may get = axioma!)

Answer 6

Hi

The problem is asking you to look at the properties of a line on a graph.

Straight lines are best analyzed in the form y= mx + c

so in your case 2x + ky = -4k can be rearranged to y = (-2/k)x -4

Then we can start looking at the questions

a) is asking for the gradient to equal 3. The gradient is the 'm' bit and equal to -2/k in your case. so solve -2/k = 3

b) is the same prinicpal, but all answers not equal to 0

c) x = 0, y = 4, so input and solve for k (original formula may be easier for this one)

d) Hint, what is the gradient when a line is horizontal. Then same as part a)

e) Trickier, again think about the gradient and what you need to set k to make it happen

Answer 7

The slop of a line is y = mx + b

For example: y = (3/2)x + 2

The slope of the line would be 3/2 meaning, on a graph you go to right 2 and up 3.

The + 2 at the end says how far up or down the line is on the y axis, in this case the line is moved up 2.

Answer 8

i think of you have some information lacking, yet right here is going... that's a 2nd order DE.... enable D = d/dt, D^2 = d^2/(dt)^2 then divide with the aid of L ... O'' +(g/L)O = 0 enable A = sqrt( g/L) then we've (D^2 + A^2)O = 0 the function eqn is r^2 + A^2 = 0 , r = sqrt(-A^2) , or r = + - iA, complicated conjugates, ... i = complicated so, O = c1(cos(At )) + c2(sin(At) ) is the ordinary answer, the place c1, c2 are constants... to come across c1, c2, we want preliminary situations.... then O ' = - c1A*(sin(At)) + c2A(cos(At)) generally you have information approximately t, O, or perhaps O ' to artwork with..... as an occasion, O = O(init), t = 0 = O' then 0 = c2A, so c2 = 0 , and O(init) = c1, so O = O(init)*cos(At) ... yet i'm not sure what to think of for O interior the subject you have given ... or a thank you to get a relation for the variables understanding in basic terms 10 min loss of time at a undeniable fee of L .... sorry .... good luck ....

Answer 9

Rewrite the equation so that y is on one side of the equal sign and everything else is on the other. That is, solve for y. Once that's done, the number in front of the x will be the slope. Now answer the questions :)

Answer 10

This is a push of of the charting Equation

y=mx+B


If you don;t understand this then have fun, as it is a lot to explain