Algebra Benchmark #2 Review

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values for the variables that makes all the equations true simultaneously.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into each equation. If both equations are satisfied, the point is a solution.

Front

What does the slope of a linear equation represent?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Front

In the equation y = mx + b, what does 'b' represent?

Back

The y-intercept, which is the value of y when x is 0.

Front

What is the meaning of the y-intercept in a real-world context?

Back

It often represents a starting value or fixed cost before any variable costs are added.

Front

What is the difference between a fixed cost and a variable cost?

Back

A fixed cost does not change with the level of output (e.g., rental fees), while a variable cost changes with the level of output (e.g., per-mile fees).

Front

How can you write an equation to model a real-world situation?

Back

Identify the variables, determine the relationship between them, and express that relationship in the form of an equation.

Front

What does the term 'linear equation' mean?

Back

A linear equation is an equation that graphs to a straight line, typically in the form y = mx + b.

Front

What is the significance of the slope in a real-world scenario?

Back

The slope indicates how much one quantity changes in relation to another, such as cost per mile in a rental scenario.

Front

How do you find the y-intercept from an equation?

Back

Set x to 0 in the equation and solve for y.