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What is the standard form of an equation of the line that passes through the points (-1,4) and (-7,-5)?

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3 Answers

"What is the standard form of an equation of the line that passes through the points (-1,4) and (-7,-5)?"
 
x--7     -7--1    -6     2
----- =  ------ = ---- = --
y--5     -5-4     -9     3
 
Multiply both sides by 3(y+5):
3(x+7) =2(y+5)
 
3x + 21 = 2y + 10
 
3x - 2y = -11

Comments

Slope is change y1 - y2 / x1 - x2 . The x values go in the denominator.
I'm not calculating slope. I'm using similar triangles and proportional parts (3 points on a line; 2 similar triangles). That's so I don't need to memorize formulas (and forget them).

Comment

First use the slope formula to get the slope.      m = ( y -  y) / (x1 - x2)
 
                                                                            m = (-5 - 4) /  (-7 - -1)
 
                                                                            m =  -9 / -6   =   9/6
 
Now use the point-slope form with the slope you just found and either of the points given:
 
   Plug in m and a point....                                      y - y1 = m (x- x1)
 
                                                                              y - 4  = 9/6 (x - -1)
 
 Simplify....                        ANSWER:                 y - 4  = 9/6 (x + 1)

Comments

Standard form is Ax + By = C or Ax + By + C = 0 depending on the author.

Comment

Hi Mikk;
(-1,4) and (-7,-5)
Let's first establish the slope.  This is the change-of-y divided by the change-of-x...
(y-y1)/(x-x1)
(4--5)/(-1--7)
Subtracting a negative number is the same as adding a positive number...
(4+5)/(-1+7)
9/6=3/2
This is the slope.
Standard equation is...
Ax+By=C, neither A nor B equal zero, and A is greater than zero.
slope=-A/B
slope=3/-2.  The two must be negative because A must be greater than zero.
3x-2y=C
Let's plug-in one coordinate to establish C...
(-1,4) and (-7,-5). I randomly select the first...
[(3)(-1)]-[(2)(4)]=C
-3-8=C
-11=C
Let's plug-in the other coordinate to verify C as -11...
3x-2y=C
[(3)(-7)]-[(2)(-5)]=C
-21-(-10)=C
-21+10=C
-11=C
 
3x-2y=-11