Finding Slope

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is calculated as the change in the y-coordinate divided by the change in the x-coordinate between two points on the line.

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 the x-coordinate increases, the y-coordinate 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-coordinate increases, the y-coordinate 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 the y-coordinate regardless of the change in the x-coordinate.

Front

What is the slope of a vertical line?

Back

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

Front

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

Back

The slope is m = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

Find the slope of the line that passes through the points (4, 5) and (4, 9).

Back

The slope is undefined because the x-coordinates are the same (4), indicating a vertical line.

Front

If a line has a slope of -3, what does this tell you about the line's direction?

Back

A slope of -3 indicates that the line falls steeply from left to right.

Front

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

Back

The slope is 2, which means for every 1 unit increase in x, y increases by 2 units.