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1. Review of Real Numbers(0)

Simplifying Fractions
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Evaluating Exponents
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Evaluating Expressions
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Translating Phrases to Expressions
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Translating Sentences to Equations
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The Distributive Property
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Simplifying Expressions
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2. Linear Equations and Inequalities(0)

The Addition and Subtraction Properties of Equality
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The Multiplication and Division Properties of Equality
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Solving Linear Equations
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Linear Inequalities in One Variable
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3. Solving Word Problems(0)

Introduction to Problem Solving
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Formulas
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Percent Problem Solving
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Mixture Problem Solving
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4. Graphing Linear Equations in Two Variables(0)

The Rectangular Coordinate System
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Graph Linear Equations in Two Variables
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Graph Linear Equations Using Intercepts
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Slope of a Line
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Slope-Intercept Form
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Point Slope Form
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5. Systems of Linear Equations(0)

Solving Systems of Linear Equations by Graphing
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Solving Systems of Linear Equations by Substitution
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Solving Systems of Linear Equations by Elimination
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6. Exponents and Polynomials(0)

The Product Rule
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The Quotient Rule
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Intro to the Power Rules
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The Power of a Quotient Rule
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Negative Exponents
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Simplifying Exponential Expressions Using All Exponent Rules
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Intro to Polynomials
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Adding and Subtracting Polynomials
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Multiplying Polynomials
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Special Products
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7. Factoring(0)

Factoring by Greatest Common Factor & Grouping
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Factoring Trinomials of the Form x² + bx + c
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Factoring Trinomials of the Form ax² + bx + c
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Factoring Special Products
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Quadratic Equations & Applications
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8. Rational Expressions and Equations(0)

Simplifying Rational Expressions
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Multiplying and Dividing Rational Expressions
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Adding and Subtracting Rational Expressions with Common Denominators
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Least Common Denominators
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Adding and Subtracting Rational Expressions with Different Denominators
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Rational Equations
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9. Inequalities and Absolute Value(0)

Set Operations and Compound Inequalities
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Absolute Value Equations
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Absolute Value Inequalities
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Linear Inequalities in Two Variables
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Systems of Linear Inequalities
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10. Relations and Functions(0)

Introduction to Relations and Functions
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Function Notation
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Graphing Common Functions
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Composition of Functions
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Direct & Inverse Variation
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11. Roots, Radicals, and Complex Numbers(0)

Introduction to Radical Expressions
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Simplifying Radical Expressions
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Adding and Subtracting Radicals
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Multiplying, Dividing, and Rationalizing Radicals
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Introduction to Complex Numbers
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Multiplying and Dividing Complex Numbers
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12. Quadratic Equations and Functions(0)

The Square Root Property
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Completing the Square
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The Quadratic Formula
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Graphing Quadratic Equations
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13. Inverse, Exponential, & Logarithmic Functions(0)

Introduction to Inverse Functions
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Exponential Functions
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Introduction to Logarithmic Functions
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Properties of Logarithms
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14. Conic Sections & Systems of Nonlinear Equations(0)

Graphing Circles
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Ellipses
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Parabolas
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Hyperbolas
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15. Sequences, Series, and the Binomial Theorem(0)

Introduction to Sequences
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Arithmetic Sequences
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Geometric Sequences
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Factorials
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4. Graphing Linear Equations in Two Variables

Graph Linear Equations in Two Variables

4. Graphing Linear Equations in Two Variables

Graph Linear Equations in Two Variables: 동영상 및 연습문제

비디오 강의 실무 워크시트

27 문제점

문제 1객관식

Which of the following is the best definition of an ordered-pair solution to a two-variable linear equation?

문제 2객관식

Why does each ordered pair (x,y) that satisfies ax + by = c correspond to a point on the graph of that equation?

문제 3객관식

Given the linear equation 3x + 2y = 12, find y when x = 2.

문제 4객관식

For the equation 2x - y = 4, compute the ordered pairs when x = -1, x = 0, and x = 3, and identify the slope of the line from those points.

문제 5객관식

The ordered pairs $open paren 1 comma 2 close paren$ , $open paren 3 comma 6 close paren$ , and $open paren 5 comma 10 close paren$ all lie on the linear equation $y equals 2 x$ . Several additional points are listed below. Which one of them must also lie on this same line? Choose the correct answer.

문제 6객관식

Which statement best explains why plotting a few ordered pairs and drawing a line through them represents infinitely many solutions to a linear equation?

문제 7객관식

Given the equation (1/2)x + y = 7, which set of x-values would be the most strategic to choose to obtain integer y-values, and why?

문제 8객관식

What is the minimum number of distinct plotted ordered pairs required to determine the unique line that represents a linear equation in two variables? Explain why.

문제 9객관식

Does the point $open paren 3 comma negative 2 close paren$ satisfy the equation $5 x + y = 13$ ? Show your algebraic check and conclusion.

문제 10객관식

Three points are given: A(1,4), B(3,8), and C(5,12). Which of the following is logically correct reasoning about whether the points lie on a single straight line?

문제 11객관식

Which of the following sets of $x$ -values is the best choice to graph the equation $7 x + 3 y = 21$ efficiently, and why?

문제 12객관식

Which coordinate on the standard coordinate plane is located three units to the right of the origin and two units down?

문제 13객관식

Which of the following correctly identifies the $x$ - and $y$ -coordinates in the ordered pair $open paren negative 4 comma 9 close paren$ ?

문제 14객관식

A student plots $open paren negative 1 comma 3 close paren$ , $open paren 0 comma 1 close paren$ , and $open paren 1 comma negative 1 close paren$ from the equation $2 x + y = 1$ and draws a line through them. Which explanation best describes why a point $open paren one half comma 0 close paren$ also belongs to the line, even though its $x$ -coordinate is not an integer?

문제 15객관식

Find y for the equation 4x - y = 5 when x = -2, x = 1, and x = 3. Provide full computation for each.

문제 16객관식

What is the $y$ -intercept of the line given by $y = - 3 x + 5$ ?

문제 17객관식

A teacher tells students to always plot at least three points before drawing the line for a linear equation. Which reason best justifies this advice?

문제 18객관식

Find x- and y-intercepts for the equation 5x + 2y = 20.

문제 19객관식

Which $x$ -values would you choose to graph $9 x + 6 y = 27$ so that you obtain integer $y$ -values, and what are the corresponding ordered pairs?

문제 20객관식

A student plotted the points $open paren 2 comma 5 close paren$ and $open paren 4 comma 11 close paren$ for a line they think comes from $3 x + y = 11$ . Is the plotted pair $open paren 4 comma 11 close paren$ consistent with this equation?

문제 21객관식

Given two points observed on a graph, $open paren 2 comma negative 1 close paren$ and $open paren 5 comma 8 close paren$ , derive the equation of the line in standard form $a x + b y = c$ with integer coefficients.

문제 22객관식

A dataset for a physical process gives the points (0,10), (2,6), and (4,2). A student claims the model is linear and predicts the value at x = 3 using interpolation. Evaluate whether this is appropriate and compute the predicted y at x = 3, showing your work.

문제 23객관식

For the equation 0.5x + y = 7, choose x = 2 and compute y.

문제 24객관식

Which point corresponds to the intersection of the horizontal line $y = - 3$ and the vertical line $x equals 4$ ?

문제 25객관식

Why is it usually sufficient to calculate and plot three ordered pairs when graphing a linear equation by hand?

문제 26객관식

Given the equation $2 x + 3 y = 12$ , compute the $y$ -values for $x equals 0$ and $x equals 3$ , and then verify whether the point $open paren 6 comma 0 close paren$ is on the same line.