An infinite gradient is a mathematical concept that describes a line with a slope that becomes increasingly steep or flat as the values of x and y approach infinity. In other words, the slope of the line becomes more and more vertical or horizontal as the distance from the origin increases.
The tangent parallel to the y/x axis is a specific type of infinite gradient. It occurs when a line is parallel to the y-axis or the x-axis, but as it approaches infinity, it becomes tangent to that axis. This creates an infinite gradient because the slope of the line is undefined in these cases.
Having a tangent parallel to the y/x axis means that the line is parallel to one of the axis (y-axis or x-axis), but as it approaches infinity, it becomes tangent to that axis. This results in an infinite gradient, where the slope of the line becomes increasingly steep or flat.
The tangent parallel to the y/x axis is calculated using the formula y = mx + b, where m is the slope of the line and b is the y-intercept. In the case of an infinite gradient, the slope (m) is undefined, resulting in a vertical or horizontal line that is tangent to the y-axis or x-axis.
Infinite gradients and tangents parallel to the y/x axis are commonly used in physics and engineering, such as in the study of electromagnetic fields or in the design of curved roads or bridges. They can also be seen in nature, such as in the shape of a tornado or a spiral galaxy.