Fall 24 Algebraic Reasoning Final Exam Review Part 1/2

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

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How do you represent a cost function for renting a car?

Back

The cost function can be represented as y = 0.75x + 35, where y is the total cost, x is the number of miles driven, and 35 is the base rental fee.

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What is the x-intercept of a function?

Back

The x-intercept is the point where the graph of a function crosses the x-axis, which occurs when y = 0. It is also known as the 'zero' of the function.

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How do you solve a system of equations?

Back

You can solve a system of equations using methods such as substitution, elimination, or graphing to find the values of the variables that satisfy all equations simultaneously.

Front

What does the equation x + y = 15 represent in a word problem?

Back

This equation represents a relationship where the total number of two types of items (e.g., horses and chickens) is 15.

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What is the meaning of the term 'zeros' in algebra?

Back

In algebra, 'zeros' refer to the values of x that make a function equal to zero, which correspond to the x-intercepts of the graph.

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What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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How do you find the slope of a line given two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

How can you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane and shade the region that satisfies all inequalities.