1. Rate of Change: The rate at which one variable changes concerning another variable.
2. Y-intercept: The point where a line crosses the y-axis on a graph.
3. Unit Rate: A rate that describes the quantity of one item in relation to one unit of another item.
4. Positive Slope: The slope of a line when it moves upward from left to right.
5. Negative Slope: The slope of a line when it moves downward from left to right.
6. Slope: The steepness of a line, indicating how much it rises or falls concerning how much it runs.
7. Proportional Relations: All the ratios of the variables are equivalent or equal.
8. Non-Proportional Relationship: The ratios of the variables are not equivalent or equal.
9. Difference in Y: The change in the y-values (vertical change) between two points.
10. Difference in X: The change in the x-values (horizontal change) between two points.
1. **Rate of Change:** The rate of change, often denoted as slope, represents the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. It indicates how much one variable changes concerning another.
2. **Y-intercept:** The y-intercept is the point where a line intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is zero.
3. **Unit Rate:** A unit rate is a specific type of rate where the denominator is 1. It describes the ratio of one quantity to one unit of another quantity, making comparisons more straightforward.
4. **Positive Slope:** A positive slope refers to the upward movement of a line from left to right on a graph. As the x-values increase, the y-values also increase.
5. **Negative Slope:** Conversely, a negative slope describes the downward movement of a line from left to right. As the x-values increase, the y-values decrease.
6. **Slope:** Slope is a general term indicating the steepness of a line. It is calculated as the ratio of the vertical change to the horizontal change between two points.
7. **Proportional Relations:** Proportional relations exist when all the ratios of the variables are equivalent or equal. This implies a constant rate of change and a linear relationship on a graph.
8. **Non-Proportional Relationship:** Non-proportional relationships occur when the ratios of the variables are not equivalent or equal. The rate of change is not constant, resulting in a nonlinear relationship.
9. **Difference in Y:** The difference in y represents the vertical change between two points on a graph. It is calculated by subtracting the y-values of two specific points.
10. **Difference in X:** Similarly, the difference in x signifies the horizontal change between two points on a graph. It is obtained by subtracting the x-values of those two points.
In summary, these terms are fundamental in understanding the behavior of linear relationships, rates of change, and the graphical representation of mathematical concepts.