Slope/Rate of Change: Tables, Graphs & 2-Points

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is 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?

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 rate of change in a linear relationship?

Back

The rate of change is the same as the slope and represents how much the dependent variable (y) changes for a unit change in the independent variable (x).

Front

If a line passes through the points (2, 3) and (5, 11), what is the slope?

Back

The slope is (11 - 3) / (5 - 2) = 8 / 3.

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-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the x-value does not change while the y-value does.

Front

How can you identify the slope from a graph?

Back

The slope can be identified by selecting two points on the line, calculating the rise (vertical change) and run (horizontal change), and then using the formula m = rise/run.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.