Slope from tables

Front

What is slope in the context of a graph?

Back

Slope is a measure of the steepness or incline of a line, calculated as the ratio of the vertical change to the horizontal change between two points on the line.

Front

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

Back

To calculate the slope from a table, use the formula: Slope (m) = (change in y) / (change in x) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

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

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, showing an inverse relationship.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-values change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as there is no horizontal change.

Front

If a line has a slope of 3, what does this mean?

Back

A slope of 3 means that for every 1 unit increase in x, the y-value increases by 3 units.

Front

What is the rate of change in a linear relationship?

Back

The rate of change is another term for slope, representing how much y changes for a unit change in x.

Front

How can you identify the slope from a graph?

Back

To identify the slope from a graph, select two points on the line, determine the rise (change in y) and run (change in x), and calculate the slope using m = rise/run.

Front

What is the slope of the line represented by the points (2, 3) and (4, 7)?

Back

Slope (m) = (7 - 3) / (4 - 2) = 4 / 2 = 2.