6.2 Linear equations in one variable  (Page 5/15)

Standard form of a line

Another way that we can represent the equation of a line is in standard form . Standard form is given as

where $A,$ $B,$ and $C$ are integers. The x- and y- terms are on one side of the equal sign and the constant term is on the other side.

Vertical and horizontal lines

The equations of vertical and horizontal lines do not require any of the preceding formulas, although we can use the formulas to prove that the equations are correct. The equation of a vertical line    is given as

where c is a constant. The slope of a vertical line is undefined, and regardless of the y- value of any point on the line, the x- coordinate of the point will be c .

Suppose that we want to find the equation of a line containing the following points: $\left(\mathrm{-3},\mathrm{-5}\right),\left(\mathrm{-3},1\right),\left(\mathrm{-3},3\right),$ and $\left(\mathrm{-3},5\right).$ First, we will find the slope.

Zero in the denominator means that the slope is undefined and, therefore, we cannot use the point-slope formula. However, we can plot the points. Notice that all of the x- coordinates are the same and we find a vertical line through $x=\mathrm{-3.}$ See [link] .

The equation of a horizontal line    is given as

where c is a constant. The slope of a horizontal line is zero, and for any x- value of a point on the line, the y- coordinate will be c .

Suppose we want to find the equation of a line that contains the following set of points: $\left(\mathrm{-2},\mathrm{-2}\right),\left(0,\mathrm{-2}\right),\left(3,\mathrm{-2}\right),$ and $\left(5,\mathrm{-2}\right).$ We can use the point-slope formula. First, we find the slope using any two points on the line.

Use any point for $\left(x_1,y_1\right)$ in the formula, or use the y -intercept.

The graph is a horizontal line through $y=\mathrm{-2.}$ Notice that all of the y- coordinates are the same. See [link] .