math
posted by emmy .
Find equation of the line that passes through the points (2/3,5/4) and (3,5/6). write your answer in slopeintercept form and standard form with integer coefficients.

The slope m of a line passing through two points (x1, y1), (x2, y2) is given by
m = (y2y1)/(x2x1)
m = (5/6  5/4) / (32/3) = (5/12) / (11/3) = 15/132 = 5/44
The equation for a straight line is of the form y = m*x + b
where m is the slope and b is the yintercept.
So far we have;
y = 5/44*x + b
To solve for b, plug in one of the points:
5/4 = 5/44 * (2/3) + b
5/4 = 10/132 + b
b = 5/4 + 10/132 = 155/132
y = 5/44*x  155/132 (slopeintercept form)
Standard form: You need to find the common factors of 44 and 132: it's 132, so multiply the equation by 132:
132*y = 15*x  155
15*x + 132*y = 155