Question

Are the equations of horizontal and vertical lines written in standard form? explain.

Answer 1

Horizontal can be written in standard form, but vertical has a challenge.

Step-by-step explanation:

Standard form of y = mx + b (slope=-intercept form, where m is the slope and b is the y-intercept, or the value of y when x is zero).

Horizonal lines can be written in standard form:

Horizonal:

Example: y = 6 is a horizontal line. In standard form, m is 0 and b is 6

y = 0*m + 6 or y = 6

Vertical lines cannot.

Vertical:

Example: x = 4 is a vertical line. In standard form, we encounter a problem. The slope, m, of a vertical line is undefined. Slope is the Rise/Run of a line. The run (change in x) is zero in this case. That means the Rise/Run is Rise/0. Division by zero is undefined. y becomes undefined, or infinity as the math-challenged like to call it (me).

Answer 2

Horizontal and vertical lines can be expressed in standard form, with a horizontal line written as y = b and a vertical line as x = a. In standard form, a horizontal line is 0x + 1y = b, and a vertical line is 1x + 0y = a.

Step-by-step explanation:

In the context of algebra and coordinate geometry, the equations for horizontal and vertical lines can indeed be written in standard form, although they are often expressed in simpler forms.

A horizontal line has a constant y-value for all points on the line.

Therefore, its equation can be expressed simply as y = b, where b is the y-intercept.

On the other hand, a vertical line has a constant x-value, and its equation is typically written as x = a, where a is the x-intercept.

The standard form for a linear equation is Ax + By = C, where A, B, and C are integers.

For a horizontal line, this becomes 0x + 1y = b (which simplifies to y = b), and for a vertical line, 1x + 0y = a (which simplifies to x = a).

These are indeed special cases of the standard form where certain coefficients are zero.

Hence, in standard form, a horizontal line is 0x + 1y = b, and a vertical line is 1x+0y = a.