Find An Equation Of A Line That Contains The Points (5,-2) And (-2,1)?


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The general equation of a line which passes through (x0,y0) is
(y - y0) = m*(x - x0)   m - is the slope of the line

slope = how many units does a close climb/descends on a specified horizontal distance

Lets consider (x0,y0) = (-2,1)
The equation of a line that passes through (-2,1) is
y-1 = m(x+2)

In order for it to pass through the second point (x1,y1)=(5,-2) we have to specify an appropriate slope.
M=(y0-y1)/(x0-x1)   -  see the definition above

so m is
m=(-2-1)/(5-(-2)) = -3/7

your answer is
y-1 = -3/7 * (x+2)

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