Graph the given linear equation. y = 1 2 x − 2 y=\frac12x-2

This problem asks us to graph the given linear equation, y equals one half x minus two. Now what I'm going to do is sketch a graph. So we're going to have a y axis, then we're going to have an x axis. Now what I'm going to do is I'm gonna choose five units up, down, to the left, and right. So we'll start on the x axis, we'll go one, two, three, four, five. In the positive x direction, we'll go one, or I'll go one, two, three, four, five in the negative x direction. Then we're going to go five units up, one, two, three, four, five in the positive y direction, and then one, two, three, four, five in the negative y direction. So we've now sketched our graph. Now, typically, when I'm doing these problems where I need to graph a linear equation, I start with an x value of negative one. But I'm actually not going to do that in this video, because I noticed that the x that we choose is going to be multiplied by one half. So what I'm actually gonna do is be strategic about this, so that way I get whole numbers. Remember, you can choose any x values that you want to. And if you wanna start with negative one, if you're just comfortable starting with negative one, then zero, then one, then two, if you're comfortable with that, that's totally fine. But I'm actually gonna show you something different for this video. I'm going to start with an x value of zero. So I'm gonna start right in the center of our graph in an x value of zero, or in the center of the x axis, I should say. And that's going to allow me to take my x and replace it with zero. So we'll get y equals one half times zero minus two. Now anything times zero will just give you zero, so we'll get zero minus two, which is negative two. So we get the point zero, negative two, which gives me a point at x is zero and y is negative two. So we have one of our points plotted. Now what I'm going to do is rather than choosing an x value of one, which might seem like the next logical step, I can see that that's gonna be multiplied by one half, which is gonna give me a fraction. So instead, I'm actually gonna choose an x value of two next, and I'm specifically gonna try to choose even numbers here. So what I'm gonna end up with is y equals one half times two minus two, because notice by choosing two as my x value rather than one, the two's actually just cancel. One half of two is just one. So we get one minus two, which is negative one. So I know when x is two, y is negative one. So at an x value of two, we're going to get a y value of negative one, which will show up on our graph. Now we would have still gotten a point that showed up on our graph if we chose one, but we would have gotten a fraction, which would have been really ugly and hard to deal with. So that's why I chose actually, this should be an x value of two. Right? Two negative one. Yeah. So that's why I chose an x value of two, right about there. Now let's choose an x value of four. Notice I'm going by even numbers here, so we're gonna choose four where our x value is gonna be at this point. And what I'm gonna do is take my x and replace it with four. So we'll have y is equal to one half times four minus two. One half of four is just two because four divided by two gives us two minus two which gives us zero. So when we have an x value of four, we have a y value of zero zero, which puts us exactly on the x axis. So this would be our point zero or our point four zero. Now notice by drawing these points, we can actually sketch a line. It's not a very steep line, but it's gonna go through these points. So this is what our graph is going to look like, and that would be the solution to this problem. So this is how you can sketch a graph, and again, you can choose the x values that you want. When I choose negative one zero one two, that's oftentimes just a safe place for me to do because I know that those are values that are going to be in that region and the math's usually not too hard to deal with. But in situations where you see a fraction and you strategically know what's going to divide and give you whole numbers or cancel, you can predict that, and that's how you can sketch your graph. You can be creative with how you choose points like I was in this one. And, again, you could have chosen negative one, zero, one, and two, and you would have still gotten the correct answer. But often, remember, you can choose whatever x values you want to to get the y values as an output and to see what your graph is gonna look like. So this is how we can graph these linear equations. Hope you found this helpful.

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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 Solving43m

Simplifying Expressions
13m

Translating Word Phrases to Algebraic Expressions
6m

Introduction to Solving Equations
21m

Translating Sentences to Algebraic Equations
2m

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 Statistics40m

Tables
12m

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3m

Frequency Distributions and Histograms
5m

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14m

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4m

8. Geometry49m

Square Roots and The Pythagorean Theorem
29m

The Circle
20m

9. Measurement58m

US Units of Length
25m

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33m

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

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33m

Special Products
34m

14. Factoring Polynomials2h 42m

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37m

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

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

Factoring Special Products
20m

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12m

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41m

15. Rational Expressions and Equations3h 13m

Simplifying Rational Expressions
39m

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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

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15m

Graphing Common Functions
5m

Composition of Functions
24m

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27m

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Set Operations and Compound Inequalities
42m

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38m

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39m

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28m

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23m

18. Roots, Radicals, and Complex Numbers3h 57m

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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

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The Square Root Property
25m

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26m

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40m

Graphing Quadratic Equations
1h 28m

20. Exponential and Logarithmic Functions2h 31m

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25m

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35m

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33m

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55m

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35m

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Introduction to Sequences
40m

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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.
$y = \frac{1}{2} x - 2$

Graph of the linear equation y equals one-half x minus two on a coordinate plane with labeled axes.

Graph showing a straight line with positive slope passing through points (-4,-4) and (4,2) on a coordinate plane.

Graph of the linear equation y equals one-half x minus two on a coordinate plane with labeled axes.

Graph of the linear equation y equals one-half x minus two, showing a line passing through points (0, -2) and (4, 0).

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Graph the given linear equation.
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