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# Input the equation of the given line in Standard form.

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

### 3 Answers by Expert Tutors

Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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!!!

You're always such a great help to me! :)
Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
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[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.
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
0
( 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