algebra EOC5

Front

What is the rate of change in a linear relationship?

Back

The rate of change is the ratio of the change in the dependent variable to the change in the independent variable, often represented as 'rise over run'. For example, if a tree grows 7 feet in 1 year, the rate of change is 7 ft/yr.

Front

How do you find the number of courses completed if given total credits and course values?

Back

Set up a system of equations based on the number of courses and their credit values. For example, if x is the number of 3-credit courses and y is the number of 4-credit courses, you can use the equations: x + y = total courses and 3x + 4y = total credits.

Front

What does the domain of a function represent?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For example, if a function is defined for x ≥ -2, then the domain is all real numbers greater than or equal to -2.

Front

How do you determine the system of equations from a graph?

Back

Identify the slopes and y-intercepts of the lines in the graph. The equations can be derived from the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Front

What happens to the graph of a function when it is transformed by subtracting a constant?

Back

Subtracting a constant from a function shifts the graph downward. For example, if g(x) = f(x) - 9, the graph of g is the graph of f shifted down by 9 units.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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/run). A positive slope indicates the line rises, while a negative slope indicates it falls.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base, and x is the exponent. It shows rapid growth or decay.

Front

What is the y-intercept of a graph?

Back

The y-intercept is the point where the graph crosses the y-axis. It occurs when x = 0. In the equation y = mx + b, the y-intercept is represented by b.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. Solutions to the system are the values that satisfy all equations simultaneously.