Calculating Slope of a Line

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the slope-intercept form of a linear equation.

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 does a zero slope indicate about a line?

Back

A zero slope indicates a horizontal line, where the y-coordinate remains constant as the x-coordinate changes.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates a vertical line, where the x-coordinate remains constant as the y-coordinate changes.

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

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

Back

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

Front

Find the slope of the line that passes through the points (0, 0) and (4, 8).

Back

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

Front

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

Back

The slope is undefined because the x-coordinates are the same.

Front

Find the slope of the line that passes through the points (5, 1) and (1, 5).

Back

m = (5 - 1) / (1 - 5) = 4 / -4 = -1.