Final answer:
To find an equation for a horizontal line, use y = k, and for a vertical line, use x = h. In the slope-intercept form y = mx + b, m is the slope and b is the y-intercept, which are crucial in defining the shape of a straight line.
Step-by-step explanation:
The equation of a vertical or horizontal line can be identified from the options given: A) y = mx + b, B) x = h, C) y = k, D) y = mx. For vertical lines, where all points on the line have the same x-coordinate but variable y-coordinates, the equation is of the form x = h. Conversely, horizontal lines, where all points share the same y-coordinate but the x-coordinate varies, are represented by the equation y = k.
Looking at the traditional slope-intercept form of a line, y = mx + b, we see that the slope m represents the rise over run, and the y-intercept b is the point where the line crosses the vertical y-axis. This formula provides a way to define the exact slope and y-intercept for straight lines, which is essential in graphically representing linear relationships.
For example, with a line represented by y = 3x + 9, the slope m is 3 and the y-intercept b is 9. This indicates that for every unit increase in x, y increases by 3 units, and the line crosses the y-axis at the point (0, 9).