Slope

Front

What is the slope?

Back

The slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change (rise) to the horizontal change (run).

Front

How do you calculate the slope between 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 an undefined slope?

Back

An undefined slope occurs in vertical lines where the change in x is zero, leading to division by zero.

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

If a line passes through the points (1, 2) and (3, 6), what is the slope?

Back

Slope = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What is the average rate of change?

Back

The average rate of change is the change in the value of a function divided by the change in the input value over an interval.

Front

If a climber ascends from 200 feet to 600 feet over 4 hours, what is the average rate of change?

Back

Average rate of change = (600 - 200) / (4 - 0) = 400 / 4 = 100 feet per hour.

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.