Linear Equation in Two Variables

I have to take a college placement test and am studying the practive test. He is the question . . . What is the equation of the line that contains the points with (x,y) coordinates (-3,7) and (5,-1)? I know that the answer is y=-x+4, but I cannot remember from high school what I do to find the answer. What is the formula?


There are various ways. One is to first get the slope m using
(x1,y1) = (-3, 7) (x2,y2) = (5,-1)
m = (y2 - y1)/(x2 - x1) = -8/8 = -1
The equation for the line can be written by forcing it to go through the point (x1,y1) with slope m:

(y - y1) = m (x - x1)
y -7 = (-1)*(x + 3)= -x -4
y = -x + 3

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  2. the pair of equation 7x+ky=k,14x+2y=k=1 represent coincident lines

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