Ohio State Test Review Algebra 1

Front

What is a linear model?

Back

A linear model is a mathematical representation of a relationship between two variables that can be expressed with a linear equation, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for y to be a function of x?

Back

For y to be a function of x, each input value (x) must correspond to exactly one output value (y). This means that no x-value can be paired with more than one y-value.

Front

How do you create an equation to model spending?

Back

To create an equation that models spending, identify the variables involved (e.g., quantity of items and price per item) and set up an equation that represents the total cost, such as Total Cost = (Price per item * Quantity) + Fixed Costs.

Front

What does an expression represent in a real-world context?

Back

An expression can represent various quantities in a real-world context, such as total cost, total distance, or total time, depending on the variables and constants included in the expression.

Front

What is an equivalent expression?

Back

An equivalent expression is a different expression that has the same value for all values of the variable(s) involved. For example, 2(x + 3) is equivalent to 2x + 6.

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). It indicates how much y changes for a unit change in x.

Front

What is the y-intercept?

Back

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

Front

How do you determine if a table represents a function?

Back

To determine if a table represents a function, check if each x-value is paired with only one y-value. If any x-value corresponds to multiple y-values, it is not a function.

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 of the variables that satisfy all equations simultaneously.

Front

What is the difference between a linear equation and a nonlinear equation?

Back

A linear equation represents a straight line when graphed and has no exponents greater than one. A nonlinear equation represents a curve and may include exponents, roots, or other non-linear terms.