Input the equation of the given line in Standard form.

Question

The line including (3, 1)and (-2, 3).

Answer 1

Hi Lindsey;

Let's begin by establishing slope.

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

m=(y-y₁)/(x-x₁)

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

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

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

m=-2/5

Standard formula...

Ax+By=C, neither A nor B equal zero, A is greater than zero...

slope of such standard formula is...

-(A/B)

-(-2/5)

A negative of a negative is positive...

2/5

2x+5y=C

Let's establish C by plugging-in one point.  I randomly select the first, (3, 1)...

[(2)(3)]+[(5)(1)]=C

6+5=11

The equation is now...

2x+5y=11

Let's verify by plugging-in the other point, (-2, 3)...

[(2)(-2)]+[(5)(3)]=11

-4+15=11

11=11

It works!!!

 

 

 

 

Answer 2

[Not drawn to scale.]

 

• (-2, 3)

|\

|  \

|    \

|____• (3, 1)

|         \
|           \
|________• (x, y)

 

Using proportional side lengths of the two similar triangles:

 

(x-(-2))/(y-3) = (3-(-2))/(1-3) = -5/2

 

Multiply both sides by 2(y-3):

 

2(x+2) = -5(y-3)

 

2x + 4 = -5y + 15

 

2x + 5y = 11

 

=====

 

Notice that using the similar triangle approach we don't have to arbitrarily define the concept of slope.

 

We can then define slope as the rate of change of y with respect to x, dy/dx.

Answer 3

( 3,1 )  ( -2, 3)

 

  Y = mx + b   / Slope intercept form.

 

   mx - y = -b    / It is standard form of equation of a line

 

 m = 3 -1 = -2/5

       -2-3

 

   -2/5 X - y = -b

 

    Plug in ( 3,1) into equation:

 

     -2/5( 3 ) - 1 = -b

 

      -6/ 5 - 1 = -b

       

       -11/ 5 = -b

   

          b = 11/5

        Plug in back to the equation:

 

          -2/5 X - Y = -11/5

 

            2X + 5Y = 11