Slope two points

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually represented by the letter '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 between two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the slope of the line through the points (3, 2) and (7, 6)?

Back

m = (6 - 2) / (7 - 3) = 4 / 4 = 1.

Front

What is the slope of the line through the points (1, 1) and (1, 4)?

Back

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

Front

What is the slope of the line through the points (0, 0) and (4, 8)?

Back

m = (8 - 0) / (4 - 0) = 8 / 4 = 2.

Front

If the slope of a line is negative, what does that indicate about the line's direction?

Back

A negative slope indicates that the line is decreasing from left to right.

Front

If the slope of a line is zero, what does that indicate about the line?

Back

A slope of zero indicates a horizontal line, meaning there is no vertical change as you move along the line.

Front

What is the slope of the line through the points (2, 3) and (5, 7)?

Back

m = (7 - 3) / (5 - 2) = 4 / 3.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

If a line has a slope of 3, what does this mean in terms of rise and run?

Back

For every 3 units of rise (vertical change), there is a corresponding run (horizontal change) of 1 unit.