Finding Slope

Front

What is the definition of slope in a linear equation?

Back

The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It is calculated as the rise over run, or the change in y divided by the change in x.

Front

How do you calculate the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

What is the slope of a horizontal line?

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 vertical line?

Back

The slope of a vertical line is undefined, as it would require division by zero (change in x is 0).

Front

How can you find the slope from a graph?

Back

To find the slope from a graph, select two points on the line, determine the rise (change in y) and run (change in x) between these points, and then use the formula slope = rise/run.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent various real-world rates, such as speed (distance over time), cost per item, or any other rate of change.

Front

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

Back

To determine the slope from a table of values, select two points (x1, y1) and (x2, y2) from the table and apply the slope formula: m = (y2 - y1) / (x2 - x1).