Question

Find equation of the line that passes through the points (2/3,-5/4) and (-3,-5/6). write your answer in slope-intercept form and standard form with integer coefficients.

Answer 1

The slope m of a line passing through two points (x1, y1), (x2, y2) is given by

m = (y2-y1)/(x2-x1)
m = (-5/6 - -5/4) / (-3-2/3) = (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 y-intercept.

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 (slope-intercept 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