The standard form for a linear equation in two variables x and y is written as Ax + By = C, where A, B, and C are constants. Let's look at how we can relate this to both horizontal and vertical lines.
Horizontal lines
The standard form for a horizontal line is y=b, where b is any real number. How can we make y=b look like Ax + By = C? What coefficient for x would cause x to be eliminated from the final equation? Let's recall the Zero Property of Multiplication.
x*0=0
Let's see what happens if we substitute A= 0, B= 1, and C= b into the standard form for a linear equation.
Therefore, we can see that the equation of a horizontal line is simply the standard form for a linear equation with A=0 and B=1.
Vertical lines
We can go through a similar process for a vertical line. The standard form for a vertical line is x=a, where a is any real number. How can we make x=a look like Ax + By = C? Let's see what happens if we substitute A= 1, B= 0, and C= a into the standard form for a linear equation.
