Find an equation of the line...?

Question

Find an equation of the line through the points (-5, 4) and (2, -5) in the general form Ax + By + C.

Help me out please?

Answer 1

One way to do it is use the this equation:  y - y1 = m (x-x1)

Where y and x (without the 1) stay in the equation- don't mess with them.  But y1 and x1 are points that you can plug in.  'm' is the slope.

y1 and x1 must be points from the same pair... so one pair is (-5, 4) and another is (2, -5).  Pick either one, and the first value is x1 and the second value is y1.  Let's pick x1= -5 and y1= -4.

Then we need the slope m, which is always rise over run, or (y2 - y1) / (x2 - x1).  This time, we need the coordinates from both sets.  

y2 = -5,  y1 = 4,  x2 = 2,  x1 = -5

Putting that into the slope equation yields m = -9/7

Now lets plug everything into our original equation:

y - 4 = -9/7 (x - (-5))

Distribute the -9/7, so:

y - 4 =  -9/7 * x - 45/7

Then take everything on one side of the equation, per the general form you specified:

-9/7x - y - 2.4285  = 0

-2.4285 is -45/7 + 4, and I just took y and -4 from the left side of the equation to the right by subtracting y from both sides and adding 4 to both sides.

To simplify things, let's multiply everything by -7, so that we get an integer for A (the value in front of x).  then we have:

9x + 7y + 17 = 0

And that does it, you've got it in the proper form.  

Hope that helps.

Answer 2

(y-y1)/(x-x1) = (y1-y2)/(x1-x2).

x1, y1 = -5, 4

x2, y2 = 2, -5.

(y-4)/(x+5) = (4+5)/(-5-2) = -9/7

y-4 = -(9/7)(x+5) = -(9x +45)/7

9x + 7y -28 + 315 =0

9x + 7y + 287 =0

Answer 3

The general equation is; (Y-b)/(X-a) = (y-b)/(x-a);

Y-4/X+5=-5-4/2+5,  (Y-4)/X+5 =3/8,8Y-32=3X+15,8Y=3X+32

3X-8Y+32=0

Answer 4

From point (-5, 4) to (2, -5), the y value decreases by 9 as the x value increases by 7. The slope of the line is -9/7.

In slope-intercept form, the equation is:

y = (-9/7)x + b

Plug in either point's x and y values to solve for the y-intercept, b:

4 = (-9/7)(-5) + b

4 = 45/7 + b

Subtract 45/7 from both sides:

28/7 - 45/7 = b

b = -17/7

The equation in slope intercept form is:

y = (-9/7)x - 17/7

Multiply both sides by 7 to clear the fractions:

7y = -9x - 17

Add 9x and 17 to both sides to get:

9x + 7y + 17 = 0