_{1})/(x-x

_{1})

**2x+5y=11**

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

Tutors, sign in to answer this question.

Hi Lindsey;

Let's begin by establishing slope.

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

m=(y-y_{1})/(x-x_{1})

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...

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

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

-4+15=11

11=11

It works!!!

[Not drawn to scale.]

• (-2, 3)

|\

| \

| \

|____• (3, 1)

| \

| \

|________• (x, y)

| \

|________• (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.

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

( 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

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