Finding Slope from Graphs and Tables

Front

What is slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b).

Front

How do you calculate the slope from two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, 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-value increases, the y-value decreases, 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 change in y as x changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it would require division by zero (change in x is 0).

Front

If a line rises 3 units for every 1 unit it runs, what is the slope?

Back

The slope is 3, calculated as rise/run = 3/1.

Front

If a line falls 2 units for every 4 units it runs, what is the slope?

Back

The slope is -1/2, calculated as rise/run = -2/4.

Front

What is the slope of the line that contains the points (1, 2) and (4, 5)?

Back

The slope is 1, calculated as (5 - 2) / (4 - 1) = 3/3 = 1.

Front

What is the slope of the line that contains the points (2, 3) and (2, 7)?

Back

The slope is undefined, as the x-values are the same (2), indicating a vertical line.