Slope from Two Points

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 ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

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

Back

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

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the change in x (run) is zero, leading to division by zero in the slope formula.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change (rise) regardless of the horizontal change (run).

Front

If a line passes through the points (2, 3) and (4, 7), what is the slope?

Back

Using the formula m = (y2 - y1) / (x2 - x1), the slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

What is the slope of the line that passes through the points (5, -10) and (5, -4)?

Back

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

Front

If a line has a slope of -1/2, what does this indicate about its direction?

Back

A slope of -1/2 indicates that for every 2 units you move to the right (positive x-direction), you move 1 unit down (negative y-direction), showing a downward slope.

Front

What is the slope of the line that passes through (-2, 8) and (0, 8)?

Back

The slope is 0 because the y-coordinates are the same, indicating a horizontal line.

Front

How can you determine if a slope is positive or negative?

Back

A positive slope means the line rises as it moves from left to right, while a negative slope means the line falls as it moves from left to right.

Front

What is the slope of a line represented by the equation y = 3x + 2?

Back

The slope is 3, which is the coefficient of x in the slope-intercept form of the equation (y = mx + b).