Slope formula and Equation Standard formula

[noel]

Hello,

I am currently trying to figure out some examples given by my instructor.

She has given me some notes that really confuse me.

During my Geometry class, I was told that a slope can rise either up or down, but it will always run to the right.

But now, for this course, my instructor gives the following information:

Use the slope to rise and run to the next point. Remember you always rise; when you run, it could be in either direction. If the slope is negative, then the run is in the negative direction. Oppositely, if the slope is positive, then run in the positive X direction.

Can anyone please help clarify this for me? She has been confusing me a whole great lot. Is there a meaning that I missed or perhaps did not get from the notes above?

Also, can someone help me how to get the answer to this?

Write an equation of a line in standard form given the following conditions:

X-intercept = -2
Y-intercept = 4

Using the intercepts, I ordered it up into pairs of

(-2, 0) and (0, 6)

And then plugged it in the slope formula to solve for the slope.

M = Y2-Y1 / X2-X1
M = 6 - 0 / 0 - (-2)
M = 6 / 2
M = 3

So now, I have the slope and the y-intercept, which I plugged into the slope-intercept formula as followed...

Y = MX + B
Y = 3X + 4

I subtracted 3X from both sides of the equation, to cancel out the 3X on the right side of the equation and to add it onto the left. So now, I have the following answer

-3X + Y = +4 (which is the standard formula)

Since A in the standard formula cannot be a negative, I multiplied the entire equation by a -1.

-1 (-3X + Y = +4)

3X - Y = -4

However, my instructor has given me the answer 2X - Y = -4

Can you please help me on how I can get the 2X and what I did that was wrong?

Thank you very much!!!

 

[galactus]

You have 2 different y-intercepts. You have a y-intercept of 4, but then used (0,6) as your coordinates.

Your coordinates, assuming the y-intercept is at y=4, should be (0,4)

Then you have two points from which you can find your equation:

(-2,0) and (0,4)

\(\displaystyle \L\\\frac{4-0}{0-(-2)}=2\)<----This is your slope, rise over run.

Using y=mx+b, where b is the y-intercept. You know it aleady. It's given.

It's y=4

So, your line equation is y=2x+4=2(x+2)

I have included a graph of the line. See how the slope is positive. It rises to the right.

 

[noel]

THANK YOU very much!!! That really helps explain a lot. Thanks!

I honestly did not know where I got the (0,6) from. Thanks so much for clarifying it.

Happy 2007!