Slope & Linear Functions

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 the vertical direction (rise) divided by the change in the horizontal direction (run).

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward trend.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward trend.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is zero, meaning there is no vertical change as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x (run) is zero, leading to division by zero.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input (x-value) has exactly one output (y-value). This can be checked using the vertical line test.

Front

What is the y-intercept of a linear function?

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 does the term 'rise over run' refer to?

Back

'Rise over run' refers to the formula for calculating slope, which is the change in y (rise) divided by the change in x (run).

Front

What is the general form of a linear equation?

Back

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