Finding Slope from Tables and Graphs

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 'm' in the equation of a line (y = mx + b). It is calculated as the change in the vertical direction (rise) divided by the change in the horizontal direction (run).

Front

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

Back

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

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, meaning the line descends from left to right.

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, meaning the line ascends from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no change in the y-values regardless of the change in x-values.

Front

What is the slope of a vertical line?

Back

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

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 their coordinates, and apply the slope formula: m = (y2 - y1) / (x2 - x1).

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 unit, or growth rates, making it essential for interpreting data.

Front

What is the slope of the line represented by the equation y = -2x + 3?

Back

The slope of the line is -2, which indicates a negative relationship between x and y.

Front

How do you interpret a slope of -3 in a real-world context?

Back

A slope of -3 means that for every unit increase in x, the value of y decreases by 3 units, indicating a strong negative relationship.