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Graphs of Linear Equations

# Standard Form of a Line

The Standard Form of a line is just another way of writing the equation of a line. It gives all of the same information as the slope-intercept form or the point-slope form.

The Standard Form of a line is in the form Ax+By=C where A is a positive integer, and B, and C are integers.

Write the equation of the line y=-3x+6 in standard form.

Solution:
First, we need to move the x-term to the left side of the equation so we add 3x to both sides. Doing this gives us:

3x + y = 6.

Here, the coefficient of the x-term is a positive integers and all other values are integers, so we are done.

Find the equation of the line with slope $\frac{4}{5}$ that passes through (-3,2)

Using the point slope form:

$y-2=\frac{4}{5}(x+3)$

$5(y-2)=5(\frac{4}{5}(x+3))$

$5y-10=4(x+3)$

$5y-10=4x+12$

$-22=4x-5y$

$4x-5y=-22$