The Standard Form of a Linear Equation

We have learned about two different types of equations for lines, slope-intercept form (y=mx+b) and point-slope form (y-y1=m(x-x1). Now we are going to learn about standard form. Standard form of an equation is Ax + By = C.

We can write equations in standard form by moving variables or constant terms, similar to what we would do if we were solving equations. Here is an example:

y = 2x - 9

If I subtract 2x from both sides then I get -2x + y = -9. Now we have an equation in standard from. Remember in class that we also discussed that we do not want fractions or decimals in our answer. We can eliminate fractions by multiplying everything in the equation by the denominator of the fraction; or, if we are dealing with decimals we can move the decimal the same amount of places to make sure that every number is whole.

We might also be given just a little information and have to use it to write an equation and then rewrite it in standard form. Here's an example:

(-8 , 3), m = 2

We can use this information to write an equation in point-slope form:

y - 3 = 2(x + 8) Do the distributive property
y - 3 = 2x + 16 Move the -3 to the other side
y = 2x + 19 Move the 2x to the other side

Answer: -2x + y = 19

Finally we discussed vertical and horizontal lines. An equation of a vertical line is always in x= form and a horizontal line is always in y= form. If we are given a point and they ask us to write an equation of a horizontal and vertical line here is what we will do:

(-4 , 4)

x = -4 Vertical line because the value of x in the coordinate is -4.
y = 4 Horizontal line because the value of y in the coordinate is 4.

I hope this has helped, let me know if you have questions.