12/17 Algebra Final Review Part 2 (Fall 24-25) Edited

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

Define slope in the context of a linear equation.

Back

Slope is a measure of the steepness of a line, represented by 'm' in the equation y = mx + b. It is calculated as the change in y divided by the change in x (rise/run).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by 'b' in the equation y = mx + b. It indicates the value of y when x is 0.

Front

How do you solve a system of linear equations using substitution?

Back

To solve a system of linear equations using substitution, solve one equation for one variable, then substitute that expression into the other equation to find the value of the second variable.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) has exactly one output (y-value). A relation can have multiple outputs for a single input.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation in the form ax^2 + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

Define a polynomial function.

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into simpler components (factors) that, when multiplied together, give the original expression.

Front

Explain the concept of a variable in algebra.

Back

A variable is a symbol (often a letter) that represents an unknown value in mathematical expressions and equations.

Front

What is the purpose of graphing a linear equation?

Back

Graphing a linear equation visually represents the relationship between the variables, allowing for easier interpretation of solutions and trends.