Who can answer this and explain why?
The graph of a linear equation passes through the points (2 , 5) and (k - 4 , k + 2).

For what values of k will the slope of the line be positive?
For what values of k will the slope of the line be negative?

What value does the slope of the line approach as k becomes a very large positive number? Why do you think that happens?

Question

Who can answer this and explain why?
The graph of a linear equation passes through the points (2 , 5) and (k - 4 , k + 2).

    For what values of k will the slope of the line be positive?
    For what values of k will the slope of the line be negative?

What value does the slope of the line approach as k becomes a very large positive number? Why do you think that happens?

tkhunny · Answer

Please calculate the general slope using the points specified.  Show us what you get, and we can talk.

anonymous · Answer

sorry i understand none of it

tkhunny · Answer

Given two points, can you calculate the slope of the line containing the two points?

Try these: (2,4) and (8,5)

anonymous · Answer

yesjust let me graph it..

anonymous · Answer

is the slope of those points 1/7 or 7/1

anonymous · Answer

use the general slope formula for "m"$$m = \frac{ y _{1} - y _{2} }{ x _{1} - x _{2} }$$and$$(x _{1}, y _{1})$$is (2, 5) and$$(x _{2}, y _{2})$$is (k - 4, k + 2)

whpalmer4 · Answer

Slope is rise/run.  For the points tkhunny gave, (5-4)/(8-2) = 1/6.  We went 6 points to the right, but only 1 point up.

tkhunny · Answer

You must be consistent.  No guessing.

Try these: (2,4) and (8,5)

$\dfrac{5-4}{8-2} = \dfrac{1}{6}$

tkhunny · Answer

Now, try these two points:  (4,2) and (Frog,Dog).  Seriously.

anonymous · Answer

Substituting:$$m = \frac{ 5 - (k + 2) }{ 2 - (k - 4) } = \frac{ 3 - k }{ 6 - k }$$

anonymous · Answer

@tkhunny can you please help me when you're done here? :)

whpalmer4 · Answer

Slope of 1 means that the line goes up at a 45 degree angle if plotted with equal size ticks on the axes.  If the slope > 1, it is steeper.  If the slope is < 1, but > 0, it is not as steep. Negative slope means it goes down as you go to the right.  Really need to have a intuitive feel for what the slope means or you'll be suffering a lot!

anonymous · Answer

Set:$$\frac{ 3 - k }{ 6 - k } > 0$$

tkhunny · Answer

Too late, tcarroll010 is doing all the work for you!  You have to be faster!

anonymous · Answer

That slope will be positive when both the numerator and denominator are the same sign.  Remember, that k cannot be 6.

anonymous · Answer

thx tcarrol, showing how to do the problem really helped

anonymous · Answer

So, the slope is positive when k < 3 or when k > 6

anonymous · Answer

Slope is negative when the numerator and denominator are of opposite signs.  So, when:

3 < k < 6

The keys to this problem are knowing and using the slope formula, identifying your points, setting up the inequality, and recognizing that you have positive slope when the top and bottom (numerator and enominator) are the same sign, and it's negative when they are of different signs.

anonymous · Answer

Thank you for your help. You explained more than my math teacher did. I really appreciate it. I'm going to close my question now but again, thanks.

anonymous · Answer

Good luck to you in all of your studies and thx for the recognition!  And you're welcome, @RedHotPickleFace

anonymous · Answer

It was nice working with you and I did give some detail here so I know you'll be able to do these now in the future.

anonymous · Answer

You have an answer now, but more importantly, you have a methodology now that you can take with you.