Graph the given linear equation. 3 x − 2 y = 4 3x-2y=4

this problem we are asked to graph the given linear equation. Now it doesn't appear that I have a graph given to me specifically in this problem, so I'm going to make my own. So we're going to have a y axis, and then we're going to have an x axis. Now on this graph, I'm going to label a few points. I like to go by five. So we're going to go one, two, three, four, five for the x axis, and we're gonna go in the negative direction, one, two, three, four, five. We're gonna go in the positive y direction, one, two, three, four, five. And then in the negative y direction, we're going to go five as well. So this is gonna be our graph. Now what I need to do is graph the equation that I see, and I can do this by choosing once. Now I'm just going to assume that this is gonna go up by one. So it's gonna go one, two, three, and this is just gonna keep going to the right, and then negative one, negative two, negative three to the left. I'm not gonna sketch those just so it doesn't look too crowded, but this is how I'm going to graph it. So going to my equation right here, what I need to do is choose x values. Now the x value I'm gonna start with is negative one. So for negative one, let's go ahead and plug this into our equation. So going to have three times negative one minus two y is equal to four. Three times negative one is negative three, and then we can add the three on both sides of the equal sign. That'll get the threes to cancel, giving me negative two y is equal to three plus four, which is seven. And then we can divide this negative two on both sides of the equation. So that's going to give us y is equal to negative seven halves. Now what this ends up coming out to, so if I go ahead and recognize that two can go into six three times, then we'll just have another half of one, so this is going to be 3.5 or negative 3.5 actually, because and that makes sense because two can divide it into six three times, and so we can divide it into seven three and a half times. So this is what we get for our y. So when x is equal to negative one, y is equal to negative 3.5. So if I go over to this graph that I sketched, well, I can see that x is negative one that we've already drawn, and I need to go down one, two, three, but then I need to go about halfway to three as well, so right about there. And notice that our point shows up on our graph, and this is going to be negative one and then negative, and then we'll go seven halves or 3.5. And so this is what our point's going to look like. Now I'm gonna choose another point. Let's say where x is zero. So in this case, we're going to have three times zero minus two y is equal to four. And that's going to give us zero minus two y equals four, which is negative two y equals four. Then divide out that negative two on both sides of the equation, giving me that y is four over negative two, which is negative two. So when x is zero, y is negative two, which is going to give me a point, and an x of zero and a y of negative two. So now I'm going to choose one more point just to secure this line, and I'm going to choose an x value of one. So So we've chosen zero, negative one, and now let's choose one. So because we have one, I'm going to plug one in for x in this equation. So that's going to give me three times one minuteus 2y is equal to four. It's going to give us three minuteus 2y equals four. I can subtract the three on both sides of the equal sign, giving me negative two y equals four minus three, which is one. And then I can divide out that negative two, which is going to get the negative twos to cancel, giving me that y is equal to negative one half. So when x is one, y is gonna be negative one half, which is the same thing as about negative 0.5. So if I go ahead and go over to my graph, when x is equal to one, y is going to be exactly on the halfway or actually, this is negative point five, so it's gonna actually be halfway down. Right? So it's gonna be halfway down, meaning that we'll have another point on our graph that we can sketch. And after sketching these points, I can just draw a line to connect them. I think three points is enough. So that's going to give me my line, and this is what we are looking for. So that will be the answer to this problem. So if you see a graph that looks like this, if you have a multiple choice, or if you just have to sketch this on a free graph, this is how you go about doing it. I went ahead and sketched the whole graph for you so you could see this process, but this is the strategy for graphing linear equations.

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1. Whole Numbers1h 55m

Multiplying Whole Numbers
46m

Dividing Whole Numbers
21m

Long Division
36m

Exponents
10m

2. Integers1h 7m

Introduction to Integers
16m

Multiplying Integers
24m

Exponential Expressions
10m

Dividing Integers
16m

3. Introduction to Solving Equations and Problem Solving Coming soon

4. Fractions1h 29m

Intro To Fractions and Mixed Numbers
44m

Simplifying Fractions
45m

5. Decimals1h 20m

Introduction To Decimals
27m

Rounding Decimals
12m

Adding And Subtracting Decimals
41m

6. Ratio, Proportion, and Percent2h 3m

Ratios and Rates
35m

Proportions
34m

Solving Percent Problems With Equations
16m

Applications of Percent
36m

7. Graphing and Introduction to Statistics Coming soon

8. Geometry49m

Square Roots and The Pythagorean Theorem
29m

The Circle
20m

9. Measurement Coming soon

10. Linear Equations and Inequalities6h 13m

The Distributive Property
17m

Review: Addition and Subtraction Properties of Equality
41m

Review: Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Introduction to Problem Solving
37m

Formulas
21m

Review: Percent Problem Solving
59m

Mixture Problem Solving
43m

Linear Inequalities in One Variable
46m

11. Graphing Linear Equations3h 17m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

12. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

13. Exponents and Polynomials3h 55m

Review: Evaluating Exponents
29m

The Product Rule
10m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

The Quotient Rule
13m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

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20m

Multiplying Polynomials
33m

Special Products
34m

14. Factoring Polynomials2h 42m

Factoring by Greatest Common Factor & Grouping
37m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
20m

Sum & Difference of Cubes
12m

Quadratic Equations & Applications
41m

15. Rational Expressions and Equations3h 13m

Simplifying Rational Expressions
39m

Multiplying And Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

16. Relations and Functions2h 9m

Introduction to Relations and Functions
57m

Function Notation
15m

Graphing Common Functions
5m

Composition of Functions
24m

Direct & Inverse Variation
27m

17. Inequalities and Absolute Value2h 52m

Set Operations and Compound Inequalities
42m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

Linear Inequalities in Two Variables
28m

Systems of Linear Inequalities
23m

18. Roots, Radicals, and Complex Numbers3h 57m

Introduction to Radical Expressions
47m

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47m

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19m

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53m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

19. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

20. Exponential and Logarithmic Functions2h 31m

Introduction to Inverse Functions
25m

Exponential Functions
35m

Introduction to Logarithmic Functions
33m

Properties of Logarithms
55m

21. Conic Sections and Systems of Nonlinear Equations2h 24m

Parabolas
35m

Graphing Circles
32m

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41m

22. Sequences, Series, and the Binomial Theorem1h 45m

Introduction to Sequences
40m

Arithmetic Sequences
27m

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26m

Factorials
11m

11. Graphing Linear Equations

Graph Linear Equations in Two Variables

Prealgebra, Beginning Algebra, & Intermediate Algebra

11. Graphing Linear Equations

Graph Linear Equations in Two Variables

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Multiple Choice

Graph the given linear equation.
$3 x - 2 y = 4$

Graph of the linear equation 3x - 2y = 4 shown as a downward sloping line on an x-y coordinate plane.

Graph of the vertical line x = 3 on a coordinate plane with labeled x and y axes.

Graph of the linear equation 3x - 2y = 4 showing a line passing through points (-2, -5) and (2, 4) on a coordinate plane.

Graph of the linear equation 3x - 2y = 4 shown as an orange line crossing the coordinate plane.

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Graph the given linear equation.3x−2y=43x-2y=4

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Graph the given linear equation.
$3 x - 2 y = 4$