Linear Equation in Two Variables
posted by J on .
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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the pair of equation 7x+ky=k,14x+2y=k=1 represent coincident lines