Slope, Domain and Range, and Relation vs. Function Review

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the ratio of the change in the y-coordinate to the change in the x-coordinate 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) 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-coordinate increases, the y-coordinate 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-coordinate increases, the y-coordinate decreases, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no change in the y-coordinate as the x-coordinate changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in the x-coordinate is 0, leading to division by zero in the slope formula.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How can you determine if a relation is a function?

Back

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

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a relation is a function by checking if any vertical line intersects the graph of the relation at more than one point.