Semester Exam Review

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It is represented as (0, b) where b is the value of the y-intercept.

Front

How do you find the slope of a linear function from its equation?

Back

The slope (m) of a linear function in the form y = mx + b is the coefficient of x. It represents the rate of change of y with respect to x.

Front

What does the term 'zero of a function' mean?

Back

The zero of a function is the value of x for which the function f(x) = 0. It is the x-coordinate of the point where the graph intersects the x-axis.

Front

What is the formula for calculating the rate of change?

Back

The rate of change is calculated as the change in the dependent variable divided by the change in the independent variable, often expressed as \( \frac{\Delta y}{\Delta x} \).

Front

What does a linear function look like on a graph?

Back

A linear function produces a straight line on a graph, characterized by a constant slope.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables. A positive slope means the function is increasing, while a negative slope means it is decreasing.

Front

How can you determine if a system of equations has no solution?

Back

A system of equations has no solution if the lines represented by the equations are parallel, meaning they have the same slope but different y-intercepts.

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, and A should be non-negative.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value).

Front

What does it mean for a function to be linear?

Back

A linear function is one that can be graphically represented as a straight line, and it has the form y = mx + b.