Slope From A Table

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change (rise) to the horizontal change (run) 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, identify two points (x1, y1) and (x2, y2) from the table, and use the formula: slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no vertical change as the horizontal change occurs.

Front

What does a positive slope indicate about the relationship between two variables?

Back

A positive slope indicates that as one variable increases, the other variable also increases, showing a direct relationship.

Front

What does a negative slope indicate about the relationship between two variables?

Back

A negative slope indicates that as one variable increases, the other variable decreases, showing an inverse relationship.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the horizontal change (run) is zero, leading to division by zero in the slope formula.

Front

If the slope between two points is 5, what does this mean in practical terms?

Back

A slope of 5 means that for every 1 unit increase in the x-direction, the y-value increases by 5 units.

Front

How can you interpret a slope of 1?

Back

A slope of 1 indicates that for every 1 unit increase in the x-direction, there is a corresponding 1 unit increase in the y-direction, representing a 45-degree angle line.

Front

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

Back

The slope can represent rates of change in various contexts, such as speed, growth rates, and trends in data.

Front

How do you determine if a slope is increasing or decreasing from a table?

Back

To determine if a slope is increasing or decreasing, calculate the slope between consecutive points; if the slope is positive, it is increasing; if negative, it is decreasing.