Write the equation of the line that contains the two points P=(−3,−2) and Q=(5,2).

Answer 1

P(-3,-2) and Q(5,2) have a line through them with slope = (2- -2)/(5- -3) = 4/8=1/2 = (y+2)/(x+2)

slope is the difference in y coordinates divided by the corresponding difference in x coordinates

y+2 = (1/2)(x+3) = x/2 +3/2

y = x/2 +3/2 -2

y = (1/2)x -1/2 is the equation in slope intercept form. slope =m=1/2, y intercept=b =3, y=mx+b

or

x -2y = 1 in standard form

or x-2y-1 = 0 in general form: ax+by+c=0 with a=1, b=-2, c=-1

check the answer.

Plug in the points:

-3 -2(-2) = -3+4 = 1

it may help to plot the 2 points on a graph, and draw a line through them, to see if your answers makes sense.

the above all assumes you're looking for a straight line.

there is an infinite number of curved lines that go through the two given points