Finding Slope

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over 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 does a slope of zero mean?

Back

A slope of zero means the line is horizontal and there is no change in the y-value as the x-value changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning the x-value does not change while the y-value does.

Front

Find the slope of the line through the points (1, 2) and (3, 6).

Back

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

Front

Find the slope of the line through the points (−9, 9) and (−2, −6).

Back

Slope = (−6 - 9) / (−2 + 9) = -15 / 7.

Front

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

Back

A slope of 1 means that for every unit increase in x, y increases by the same amount, resulting in a 45-degree angle line.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.