Introduction to slope

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually represented 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 does a positive slope indicate about a line?

Back

A positive slope indicates that as you move from left to right along the line, the line rises.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as you move from left to right along the line, the line falls.

Front

What does a slope of zero mean?

Back

A slope of zero means the line is horizontal and there is no vertical change as you move along the line.

Front

What does an undefined slope mean?

Back

An undefined slope occurs with vertical lines, where the change in x is zero, leading to division by zero in the slope formula.

Front

If a line has a slope of 1, what does this imply?

Back

A slope of 1 implies that for every unit increase in x, there is a corresponding unit increase in y, resulting in a 45-degree angle with the x-axis.

Front

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

Back

Using the slope formula, m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

How do you interpret a slope of -3/5?

Back

A slope of -3/5 means that for every 5 units you move to the right (positive x-direction), the line moves down 3 units (negative y-direction).

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.