Calculate Slope from 2 Points & y=mx+b

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) 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 a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in y as x changes.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant 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, resulting in a downward slant from left to right.

Front

What is the slope of the line through the points (2, 3) and (4, 7)?

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 through the points (1, 1) and (1, 5)?

Back

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

Front

What is the slope-intercept form of a line?

Back

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

Front

How do you find the y-intercept from the equation y = 2x + 3?

Back

The y-intercept is the value of y when x = 0. For the equation y = 2x + 3, when x = 0, y = 3.

Front

What is the equation of a line with a slope of 3 that passes through the point (0, 2)?

Back

Using the slope-intercept form, the equation is y = 3x + 2.