Define each one with a simple answer

Question

Slope as rate of change
Slope as a unit rate
Slope using Similar Triangles
Comparing proportional relationships in tables, graphs and equations

Answer 1

1. Slope as rate of change: Slope measures how much one variable changes in relation to another variable. It tells us the steepness or incline of a line on a graph.

2. Slope as a unit rate: Slope can also be understood as a ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. This ratio, which can be expressed as a fraction or decimal, represents the slope as a unit rate.

3. Slope using Similar Triangles: In some cases, the slope of a line can be determined by comparing the lengths of corresponding sides of similar triangles formed by the line and the x- and y-axes. By comparing the side lengths, we can find the ratio of the rise to the run, which gives us the slope.

4. Comparing proportional relationships in tables, graphs, and equations: This involves examining different representations (such as tables, graphs, and equations) to determine if they exhibit proportional relationships, which are characterized by a constant ratio between two variables. By comparing the values or patterns in these different representations, we can identify and compare proportional relationships.