Module 2 Topic 1 Graphing Part 1

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you calculate the first differences in a table of values?

Back

First differences are calculated by subtracting each y-value from the subsequent y-value in the table. If the first differences are constant, the relationship is linear; if they vary, the relationship is non-linear.

Front

What does it mean if a function increases over its entire domain?

Back

If a function increases over its entire domain, it means that as the x-values increase, the y-values also increase without any decrease at any point.

Front

What is an x-intercept?

Back

An x-intercept is the point where a graph crosses the x-axis, meaning the y-value at that point is zero. It is represented as (x, 0).

Front

What does the y-intercept represent in a real-world context?

Back

The y-intercept represents the value of y when x is zero. In a real-world context, it often indicates the starting value of a quantity before any changes occur.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for calculating the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What is a linear relationship?

Back

A linear relationship is one where the graph of the relationship forms a straight line, indicating a constant rate of change between the variables.

Front

What is a non-linear relationship?

Back

A non-linear relationship is one where the graph does not form a straight line, indicating that the rate of change between the variables is not constant.

Front

How can you determine if a table represents a linear relationship?

Back

You can determine if a table represents a linear relationship by calculating the first differences; if they are constant, the relationship is linear.

Front

What are key features to look for in the graphs of functions?

Back

Key features include intercepts, slope, whether the function is increasing or decreasing, and the overall shape of the graph (linear or non-linear).