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Input the equation of the given line in Standard form.

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3 Answers

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!!!
 
 
 
 

Comments

[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.
( 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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