Question

what does it mean when your slope is an integer?

Explanation:

The slope of a line is calculated as \( m=\frac{\text{change in } y}{\text{change in } x}=\frac{\Delta y}{\Delta x} \). When the slope \( m \) is an integer, it means that for every 1 - unit increase in the \( x \) - value (horizontal change), the \( y \) - value (vertical change) changes by that integer number of units. For example, if the slope \( m = 2 \), then for each increase of 1 in \( x \), \( y \) increases by 2. If the slope \( m=- 3 \), for each increase of 1 in \( x \), \( y \) decreases by 3. In terms of the line's graph, an integer slope indicates a constant rate of change between the \( x \) and \( y \) variables, and the line will have a "steepness" corresponding to the magnitude of the integer (with positive integers indicating an upward - sloping line from left to right and negative integers indicating a downward - sloping line from left to right).

Answer:

When a slope is an integer \( m \), for every 1 - unit change in \( x \) (horizontal change), the \( y \) - value (vertical change) changes by \( m \) units. It represents a constant rate of change between \( x \) and \( y \), with the line's steepness and direction (upward for \( m>0 \), downward for \( m < 0 \)) determined by the integer's value and sign.