Question

read the passage and answer the following question
module vocabulary
absolute value function
constant function
equation
family of graphs
identity function
parameter
parent function
rate of change
reflection
simple interest
slope
transformation
translation
vertex
the slope of a line is the rate of change in the y-coordinates (rise) to the corresponding change in the x-coordinates (run) for points on the line.
true
false

Explanation:

Step1: Recall Slope Definition

The slope of a line is defined as the ratio of the change in \( y \)-coordinates (rise, \( \Delta y \)) to the change in \( x \)-coordinates (run, \( \Delta x \)) between two points on the line. Mathematically, slope \( m=\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1} \), which is the rate of change of \( y \) with respect to \( x \).

Step2: Compare with Given Statement

The statement says "The slope of a line is the rate of change in the \( y \)-coordinates (rise) to the corresponding change in the \( x \)-coordinates (run) for points on the line." This matches the definition of slope (rate of change of \( y \) over \( x \), i.e., rise over run).

Answer:

True