A line passes through the points $P$ and $Q.$ If $P = (-8,2)$ and $Q = (4,-7),$ then write the equation of this line in the form $Ax + By = C,$ where $A$, $B$, and $C$ are integers with greatest common divisor $1,$ and $A$ is positive.

jaekg Aug 12, 2024

#1**+1 **

First, find the slope between the two points:

slope M = (y1-y2) / (x1-x2) = (2 - -7 ) /(-8-4) = - 9 / 12 = - 3/4

Now the line in y = Mx + b form becomes

Y = -3/4 x + b Sub in either point to find 'b' = -4

then the line equation is Y = =-3/4 x - 4

Re-arrange to

3/4 x + y = -4 Multiply thru by 4

3x + 4y = -16 Done .

ElectricPavlov Aug 12, 2024