Slope from a GRAPH

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness or incline of a line, calculated 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 between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does a positive slope indicate about a line on a graph?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line on a graph?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the line falls from left to right.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates a vertical line, where the x-values are constant and the line does not rise or fall.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that the y-values remain constant as the x-values change.

Front

If a line has a slope of -2/1, what does this tell you about the line's steepness and direction?

Back

A slope of -2/1 indicates that for every 1 unit the line moves to the right, it moves down 2 units, making it a steep line that falls from left to right.

Front

What is the slope of a line that rises 4 units for every 5 units it runs to the right?

Back

The slope of the line is 4/5, indicating a positive slope that rises from left to right.

Front

How can you determine if a slope is positive, negative, or undefined from a graph?

Back

You can determine the slope by observing the direction of the line: if it rises, the slope is positive; if it falls, the slope is negative; if it is vertical, the slope is undefined.

Front

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

Back

The slope can represent rates of change, such as speed, growth, or decline, and is used in various fields like physics, economics, and engineering.