Slope

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 formula to calculate the slope (m) between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning it does not rise or fall.

Front

Calculate the slope of the line that passes through the points (2, 3) and (4, 7).

Back

m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

If a line has a slope of -1, what does this tell you about its direction?

Back

A slope of -1 indicates that the line descends from left to right.

Front

What is the average rate of change in a situation where a climber goes from 400 feet to 700 feet in 4 hours?

Back

Average rate of change = (700 - 400) / (6 - 2) = 300 / 4 = 75 feet per hour.

Front

Find the slope of the line that passes through the points (10, 1) and (5, 2).

Back

m = (2 - 1) / (5 - 10) = 1 / -5 = -1/5.

Front

What is the slope of a line that rises 3 units for every 2 units it runs?

Back

The slope is 3/2.

Front

If the slope of a line is 2, what does this mean in terms of rise and run?

Back

For every 2 units the line rises, it runs 1 unit horizontally.