How many dimensions do linear equations on the x-y plane have?
Linear equations on the x-y plane have two dimensions.
To understand why, let's break it down. The x-y plane, also known as the Cartesian plane, is a graph formed by two perpendicular number lines, one horizontal (representing the x-axis) and the other vertical (representing the y-axis). Each point on this plane is identified by a unique pair of coordinates (x, y), where x represents the position on the x-axis and y represents the position on the y-axis.
Now, linear equations on the x-y plane represent straight lines. These equations can be written in the form y = mx + b, where m represents the slope (the rate of change of y with respect to x) and b represents the y-intercept (the point where the line crosses the y-axis).
Since a straight line in the x-y plane can be completely determined by the slope (m) and the y-intercept (b), it means that choosing a specific pair of values for m and b will give you a unique line. This effectively means that linear equations on the x-y plane have two dimensions, one for the x-axis and one for the y-axis, as changing the values of m and b can change the position and the slope of the line.