HELPING FINDING EQUATION USING 4,1 AND -2,3

Question

PLEASE HELP ME SOLVE TO FIND THE EQUATION IN STANDARD FORM.  I have the slope as 3/-6.  Points are 4,1 and -2,3

 

I started with     3(y-1) = -6(x-3)                       3(y-4) = -6(x - (-2)

                    =  3y-3 = -6x + 18                       3y-12 = -6x -12

                    =  3y + 6x = 21                           3y + 6x = 0

 

 

Please help beause the two equations are not the same

                

Answer 1

There's a couple of other issues besides having an incorrect slope.

 

One is how the slope has been applied to the m (x - x) = (y - y) equation.  Notice the slope is actually on the side with the x's. 

 

slope = rise/over

 

m = (y - y)/(x - x)

 

If you were to multiply both sides by (x - x), you end up with m(x - x) = (y - y).  (That's how that point/slope equation is derived.)

 

I don't know if you learned to split a fraction across the two halves of that equation, or you just aren't showing that step, but let's show the steps.  If your slope were 1/2, it would be:

 

(1/2)(x - x) = (y - y)

 

You could then multiply both sides by that 2 in the denominator in order to get rid of that fraction:

 

(2)[(1/2)(x - x)] = (y - y)(2)

 

The 2 on the left cancels out the 2 in the denominator and you'd be left with:

 

1 (x - x) = 2 (y - y)

 

If you're trying to shortcut that somehow, notice it's the numerator that ended up with the x's and the denominator that ended up with the y's.  You have that the other way around. 

 

Also, you're not being consistent with the points.  This is really, really easy to mess up.

 

Your points are (4,1) and (-2,3).

 

In your left equation you used 1 for y and 3 for x.  The 1 is the y from the first point.  The 3 is the y from the second point, not the x.  If you use the y from the first point, you must use the x from the first point as well; hence, 1 for the y and 4 for the x.  (y - 1) and (x - 4)

 

On the right equation, you used 4 for y and -2 for x.  The -2 for x would be correct, but since that point is (-2,3), the matching y is 3.  (y - 3) and (x - (-2)).

 

Do you see what I mean?  You were using the y's in the left equation and the x's in the right equation, rather than one point in each equation.

 

Again, that's very easy to mix up, so you have to pay close attention.

Answer 2

Hi L;

4,1 AND -2,3

First, let's establish slope.

Slope is change-of-y divided by change-of-x...

m=(y-y₁)/(x-x₁)

m=(1-3)/(4--2)

Subtracting a negative number is the same as adding a positive number...

m=(1-3)/(4+2)

m=-2/6=-1/3

Standard formula is...

Ax+By=C, A>0

Slope of such is -A/B...-(-1/3)...

A negative of a negative is positive...

x+3y=C

Let's establish the value of C by plugging-in either coordinate.  I randomly choose the first...

4,1

x+3y=C

4+[(3)(1)]=C

7=C

x+3y=7

Let's plug-in the other coordinate to verify...

-2,3

x+3y=7

-2+[(3)(3)]=7

-2+9=7

7=7

Answer 3

The slope, m, is (3-1)/(-2-4) = 2/(-6) = -1/3, not -1/2.  If you use the correct value of the slope, the equations will agree.