Comparing Rates of Change

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the slope, which represents the ratio of the change in the y-value to the change in the x-value.

Front

How do you determine the slope of a linear function from a graph?

Back

The slope can be determined by selecting two points on the line, calculating the rise (change in y) and run (change in x), and then using the formula: slope = rise/run.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

How can you compare the slopes of two linear functions?

Back

You can compare the slopes by looking at their numerical values; the function with the larger slope value has a greater rate of change.

Front

What is the slope of a line that is horizontal?

Back

The slope of a horizontal line is 0, indicating no change in the y-value as the x-value changes.

Front

What is the slope of a line that is vertical?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero.

Front

If a function has a slope of 2, what does this mean?

Back

A slope of 2 means that for every 1 unit increase in x, the y-value increases by 2 units.

Front

How do you find the slope from a table of values?

Back

To find the slope from a table, select two points (x1, y1) and (x2, y2) and use the formula: slope = (y2 - y1) / (x2 - x1).