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 to the horizontal change between two points on the line.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value 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-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning there is no horizontal change (the denominator is zero), and thus the slope cannot be calculated.

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 is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-value changes.

Front

If a line has a slope of 5/2, what does this mean in terms of rise over run?

Back

A slope of 5/2 means that for every 2 units of horizontal change (run), the line rises 5 units (rise).

Front

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

Back

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

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x is 0.

Front

How can you determine if a slope is positive, negative, or undefined from a graph?

Back

A positive slope rises from left to right, a negative slope falls from left to right, and an undefined slope is represented by a vertical line.