Finding the Slope of Lines

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is calculated as the change in y (rise) divided by the change in x (run).

Front

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

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y 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 x increases, y decreases, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no change in y regardless of the change in x.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in x is 0, leading to division by zero.

Front

Find the slope of the line that passes through the points (2, 3) and (5, 7).

Back

The slope is (7 - 3) / (5 - 2) = 4 / 3.

Front

If a line has a slope of -2, what does this tell you about the line's direction?

Back

A slope of -2 indicates that the line falls steeply from left to right.

Front

What is the slope of the line represented by the equation y = 3x + 1?

Back

The slope is 3, which means for every 1 unit increase in x, y increases by 3 units.

Front

What is the slope of the line represented by the equation y = -1/2x + 4?

Back

The slope is -1/2, indicating the line falls as x increases.