Slope Practice

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 do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be 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 the x-values increase, the y-values also increase, 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-values increase, the y-values decrease, meaning the line falls from left to right.

Front

What is an undefined slope?

Back

An undefined slope occurs when a line is vertical, meaning it has no horizontal change (run = 0), resulting in division by zero.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no vertical change as the x-values change.

Front

How can you determine the type of slope from a graph?

Back

You can determine the type of slope by observing the direction of the line: if it rises, the slope is positive; if it falls, the slope is negative; if it is horizontal, the slope is zero; and if it is vertical, the slope is undefined.

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 do you find the slope from a linear equation in standard form?

Back

To find the slope from a linear equation in standard form (Ax + By = C), rearrange it to 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 unit, or growth rates, making it essential for interpreting data and making predictions.