explain to me why the slant of a line with slope 5/3 is steeper than the slant of a line with slope 4/3

The steeper the line, the larger the slope

since 5/3 is greater than 4/3, consider it explained

To explain why the slant of a line with slope 5/3 is steeper than the slant of a line with slope 4/3, let's first understand what slope represents.

In geometry, the slope of a line is a measure of its steepness. It indicates how much the line rises (vertical distance) or falls (vertical change) for a given horizontal distance. The slope is calculated as the change in the y-coordinates divided by the change in the x-coordinates between any two points on the line.

For instance, let's consider the line with a slope of 5/3. This means that for every 3 units the line moves horizontally (change in x-coordinate), it moves 5 units vertically (change in y-coordinate) in the positive direction (upward). This indicates a steeper slant as it ascends at a faster rate compared to the line with a slope of 4/3.

On the other hand, the line with a slope of 4/3 means that for every 3 units it moves horizontally, it moves 4 units vertically. Although it rises, it does so at a slower rate than the line with a slope of 5/3. Therefore, the slant of the line with a slope of 5/3 is steeper.

In general, the larger the numerator (change in y-coordinates) or the smaller the denominator (change in x-coordinates), the steeper the line's slant will be. This relationship holds true as long as the slopes being compared have the same sign (both positive or both negative).

To determine the steeper line when given the slopes, you can compare the values directly, or convert them to a common denominator if necessary.