What problems might you encounter when calculating the equation of a line whose graph is actually parallel to one of the axes?
The answer states, "Horizontal lines have any y-value and vertical lines have any x-value."
Could anyone explain this, I'm not sure if I fully understand it. Thanks.
take the graph 2y+Ox=10
try to plot it. It is a horizontal line, y=5. There is not a single x value.
Ohhhh, that makes sense. Thanks :>
Sure! To understand why horizontal lines have any y-value and vertical lines have any x-value, let's first clarify what it means for a line to be parallel to one of the axes.
When a line is parallel to the x-axis (horizontal), it means that no matter how far you move left or right (along the x-axis), the y-coordinate remains the same. In other words, the y-value is constant for all points on the horizontal line. Conversely, when a line is parallel to the y-axis (vertical), it means that no matter how far you move up or down (along the y-axis), the x-coordinate remains the same. In other words, the x-value is constant for all points on the vertical line.
Now, let's consider the equation of a line in general, given by the formula y = mx + b, where m is the slope and b is the y-intercept. When a line is horizontal (parallel to the x-axis), it means that the slope (m) is zero because the y-value does not change as x changes. In this case, the equation of the line becomes y = 0x + b, which simplifies to y = b. This means that any y-value (b) can be the equation of a horizontal line.
On the other hand, when a line is vertical (parallel to the y-axis), the slope (m) is undefined because the x-value does not change as y changes. In this case, there is no x-term in the equation of the line. So, the equation becomes x = a, where a is any x-value on the vertical line. This means that any x-value (a) can be the equation of a vertical line.
In summary, for lines that are parallel to one of the axes, horizontal lines can have any y-value, and vertical lines can have any x-value.