# geometry

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If the slope of a line is 5/3 and a point on the line is (57,12) using the given point and the slope find the coordinates of the lattice point on the line?

• geometry -

The "point-slope" form of the equation of a straight line is:

y - y1 = m ( x - x1 )

(x1, y1) is a known point

m is the slope of the line

(x, y) is any other point on the line

In this case:

m = 5 / 3 , x1 = 57 , y1 = 12

y - 12 = ( 5 / 3 ) (x - 57 )

y = (5 x / 3 ) - ( 5 * 57 / 3 ) + 12

y = (5 x / 3 ) - ( 285 / 3 ) + 12

y = (5 x / 3 ) - 95 + 12

y = (5 x / 3 ) - 83

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