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# How to Graph Linear Equations with Fractions?

TopResolving the Linear Equations in Math is not a very difficult task. By this we are able to find the values of the unknowns in the equation. We may come across situations where Fractions are contained within the linear equations. In such cases we need to first bring the equation in a proper form by applying certain operations and then we solve them further. To graph such equations we have to bring the equation in normal form i.e. standard form of line.

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: