Algebra I Regents Aug-22 (1-24) English

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, 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 of a linear equation?

Back

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

Front

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

Back

To solve a system 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 does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect, meaning they have no points in common.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation ax^2 + bx + c = 0, and 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 the difference between a monomial and a binomial?

Back

A monomial is an algebraic expression with one term, while a binomial has two terms separated by a plus or minus sign.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression, look for two numbers that multiply to give the constant term and add to give the coefficient of the linear term, then express it as (x + p)(x + q).