x and y intercepts, types of 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 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 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

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the slope-intercept form.

Front

How can you identify the y-intercept from a graph?

Back

The y-intercept can be identified as the point where the line intersects the y-axis.

Front

What is the significance of the y-intercept in a real-world context?

Back

The y-intercept often represents the starting value or initial condition in a real-world scenario, such as the initial amount of money in a bank account.

Front

What is the relationship between slope and rate of change?

Back

Slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Front

What does a slope of zero indicate about a line?

Back

A slope of zero indicates a horizontal line, meaning there is no change in the y-value as the x-value changes.