Finding Slope from a Table & Graph Giraldi

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 two points (x1, y1) and (x2, y2)?

Back

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

Front

What does a slope of zero indicate about a line?

Back

A slope of zero indicates that the line is horizontal, meaning there is no vertical change as you move along the line.

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 change in x (run) is zero, leading to division by zero in the slope formula.

Front

How can you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, find the rise (vertical change) and run (horizontal change) between them, and use the slope formula.

Front

What is the slope of a line that rises 4 units for every 3 units it runs?

Back

The slope of the line is 4/3.

Front

If a line has a slope of -1/2, what does this tell you about its direction?

Back

A slope of -1/2 indicates that the line descends from left to right, meaning it decreases as you move along the x-axis.

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, cost per item, or growth rates.