Rate of Change and Slope

Front

What is the definition of rate of change?

Back

The rate of change is a measure of how much a quantity changes in relation to another quantity, often expressed as a ratio or fraction.

Front

How do you calculate the rate of change between two points (x1, y1) and (x2, y2)?

Back

Rate of change = (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.

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.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If a line has a slope of -1, what does this mean?

Back

It means that for every unit increase in x, there is a one unit decrease in y.

Front

Calculate the slope of the line that passes through the points (2, 3) and (5, 11).

Back

Slope = (11 - 3) / (5 - 2) = 8 / 3.

Front

What is the formula for slope-intercept form of a line?

Back

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

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis (x=0).