Let us consider an example to learn how to graph linear equations with fractions. Suppose we have an equation given as: (4 y + 5 x - 1) /3 = (8 y - x + 5) /4, bring the equation in standard form i.e. y = mx + c:

We first cross multiply the terms in the equation to get:

(4 y + 5 x - 1) /3 = (8 y - x + 5) /4,

4 (4 y + 5 x - 1) = 3 (8 y - x + 5),

Or 16 y + 20 x – 4 = 24 y -3x + 15,

Or 8y = 23 x – 19,

Or y = 23 /8 x - 19 /8............ equation 1.

Slope of equation, on comparing it with standard form is m = 23 /8 and intercept is c = -19 /8.

Substituting the random values of 'x' in equation 1 we get:

x =0, y = -19 /8,

x = 1, y = 1 /2,

x = -1, y = 21 /4,

x = 2, y = 25 /8,

This way we can find the values of 'y' for arbitrary values of 'x'. This gives us the required graph of equation: y = 23 /8 x - 19 /8 as: