Finding Slope from a Graph

Front

What is the definition of slope in a graph?

Back

The slope of a line is a measure of its steepness, 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 from 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?

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?

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 is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-values change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it represents a division by zero in the slope formula.

Front

If a line rises 3 units for every 4 units it runs, what is the slope?

Back

Front

If a line falls 2 units for every 5 units it runs, what is the slope?

Back

Front

How can you identify the slope from a graph visually?

Back

You can identify the slope by selecting two points on the line, measuring the vertical rise and horizontal run between them, and calculating the ratio.

Front

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

Back

The slope is 2, which means for every 1 unit increase in x, y increases by 2 units.