Algebra Semester 1 Review 2022-2023 (Units 1-6)

Front

What is the average rate of change?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value. It can be calculated using the formula: \( \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \)

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect. For example, the lines represented by the equations \( y = mx + b_1 \) and \( y = mx + b_2 \) are parallel.

Front

How do you express '7 times the difference of y and 4' in algebraic form?

Back

The expression is written as \( 7(y - 4) \).

Front

What is the solution to the inequality \(-10 \le \frac{4x - 5}{2} < 20\)?

Back

The solution is \(-3 \frac{3}{4} \le x < 11 \frac{1}{4}\).

Front

What is the difference between causation and association?

Back

Causation indicates that one event is the result of the occurrence of another event, while association indicates a relationship between two variables without implying that one causes the other.

Front

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

Back

The slope \( m \) can be calculated using the formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \) where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.

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 does it mean for a function to be linear?

Back

A function is linear if it can be graphically represented as a straight line. It has the form \( y = mx + b \), where m is the slope and b is the y-intercept.

Front

How do you solve a linear equation for a variable?

Back

To solve for a variable, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis. It can be found by setting \( x = 0 \) in the equation of the line.