Slope

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

Front

How is slope calculated between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down and does not have a defined angle.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as you move along the line.

Front

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

Back

A slope of -2 indicates that for every 2 units the line moves down vertically, it moves 1 unit to the right horizontally, resulting in a downward slope.

Front

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

Back

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

Front

How can you determine the slope from a linear equation in standard form Ax + By = C?

Back

To find the slope from the standard form, rearrange the equation into slope-intercept form (y = mx + b) and identify the coefficient of x as the slope.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change in various contexts, such as speed, cost per item, or growth rates, helping to analyze relationships between variables.

Front

How do you find the slope of a line given two points with the same x-coordinate?

Back

If two points have the same x-coordinate, the slope is undefined because it results in division by zero when calculating (y2 - y1) / (x2 - x1).

Front

What is the slope of the line represented by the equation y = 3x + 4?

Back

The slope of the line is 3, as it is the coefficient of x in the slope-intercept form.