Understanding Functions and Slope

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run).

Front

How do you find 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 the y-intercept represent in a linear equation?

Back

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

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.

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

How can you determine if a set of ordered pairs represents a function?

Back

A set of ordered pairs represents a function if no two pairs have the same first element (x-value).

Front

What is the significance of a negative slope?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

What is the significance of a positive slope?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What is the formula for calculating the y-intercept from a linear equation?

Back

To find the y-intercept (b) from the slope-intercept form y = mx + b, set x = 0 and solve for y.