Slope and Rate of Change

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change to the horizontal change between two points on the line.

Front

What is the slope formula?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the change in x is zero, leading to division by zero in the slope formula.

Front

What does a slope of zero indicate?

Back

A slope of zero indicates a horizontal line, where there is no vertical change as x changes.

Front

Calculate the slope between the points (1, 2) and (3, 6).

Back

The slope is 2, calculated as (6 - 2) / (3 - 1).

Front

Calculate the slope between the points (4, 5) and (4, 1).

Back

The slope is undefined, as the x-coordinates are the same, indicating a vertical line.

Front

If a line has a slope of 3, what does this mean?

Back

A slope of 3 means that for every 1 unit increase in x, the value of y increases by 3 units.

Front

What is the slope of a line that goes down from left to right?

Back

The slope of a line that goes down from left to right is negative.

Front

Find the slope of the line represented by the equation y = 2x + 1.

Back

The slope of the line is 2.

Front

What is the relationship between slope and rate of change?

Back

Slope represents the rate of change of y with respect to x; it shows how much y changes for a unit change in x.