Choose The Best Graph That Represents The Linear Equation:$-2x - 16y = -8$A. Graph A B. Graph B

Introduction

Linear equations are a fundamental concept in mathematics, and graphing them is an essential skill for students and professionals alike. In this article, we will explore how to choose the best graph to represent a linear equation, specifically the equation $-2x - 16y = -8$. We will examine two possible graphs, A and B, and determine which one accurately represents the given equation.

Understanding Linear Equations

A linear equation is an equation in which the highest power of the variable(s) is 1. In the equation $-2x - 16y = -8$, the highest power of $x$ and $y$ is 1. This means that the graph of the equation will be a straight line.

Graphing Linear Equations

To graph a linear equation, we need to find two points on the line. We can do this by substituting values of $x$ and $y$ into the equation and solving for the other variable. Let's find two points on the line represented by the equation $-2x - 16y = -8$.

Finding Point 1

Let's substitute $x = 0$ into the equation and solve for $y$.

$$-2(0) - 16y = -8$$

$$-16y = -8$$

$$y = \frac{-8}{-16}$$

$$y = \frac{1}{2}$$

So, the point $(0, \frac{1}{2})$ is on the line.

Finding Point 2

Let's substitute $y = 0$ into the equation and solve for $x$.

$$-2x - 16(0) = -8$$

$$-2x = -8$$

$$x = \frac{-8}{-2}$$

$$x = 4$$

So, the point $(4, 0)$ is on the line.

Graph A

Graph A is a straight line with a slope of $\frac{1}{4}$ and a y-intercept of $\frac{1}{2}$. The line passes through the points $(0, \frac{1}{2})$ and $(4, 0)$.

Graph B

Graph B is a straight line with a slope of $-\frac{1}{8}$ and a y-intercept of $-\frac{1}{2}$. The line passes through the points $(0, -\frac{1}{2})$ and $(4, 0)$.

Choosing the Best Graph

Now that we have examined both Graph A and Graph B, we need to determine which one accurately represents the equation $-2x - 16y = -8$. To do this, we can substitute the coordinates of the points on each graph into the equation and see which one satisfies the equation.

Substituting Point 1 into Graph A

Let's substitute the point $(0, \frac{1}{2})$ into the equation $-2x - 16y = -8$.

$$-2(0) - 16(\frac{1}{2}) = -8$$

$$-8 = -8$$

This shows that the point $(0, \frac{1}{2})$ is on the line represented by Graph A.

Substituting Point 2 into Graph A

Let's substitute the point $(4, 0)$ into the equation $-2x - 16y = -8$.

$$-2(4) - 16(0) = -8$$

$$-8 = -8$$

This shows that the point $(4, 0)$ is also on the line represented by Graph A.

Substituting Point 1 into Graph B

Let's substitute the point $(0, -\frac{1}{2})$ into the equation $-2x - 16y = -8$.

$$-2(0) - 16(-\frac{1}{2}) = -8$$

$$8 = -8$$

This shows that the point $(0, -\frac{1}{2})$ is not on the line represented by Graph B.

Substituting Point 2 into Graph B

Let's substitute the point $(4, 0)$ into the equation $-2x - 16y = -8$.

$$-2(4) - 16(0) = -8$$

$$-8 = -8$$

This shows that the point $(4, 0)$ is on the line represented by Graph B.

Conclusion

Based on our analysis, we can see that Graph A accurately represents the equation $-2x - 16y = -8$. The line passes through the points $(0, \frac{1}{2})$ and $(4, 0)$, and the equation is satisfied for both points. Graph B, on the other hand, does not accurately represent the equation, as the point $(0, -\frac{1}{2})$ is not on the line.

Final Answer

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Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In the equation $-2x - 16y = -8$, the highest power of $x$ and $y$ is 1.

Q: How do I graph a linear equation?

A: To graph a linear equation, you need to find two points on the line. You can do this by substituting values of $x$ and $y$ into the equation and solving for the other variable.

Q: What are the two points on the line represented by the equation $-2x - 16y = -8$?

A: The two points on the line represented by the equation $-2x - 16y = -8$ are $(0, \frac{1}{2})$ and $(4, 0)$.

Q: Which graph accurately represents the equation $-2x - 16y = -8$?

A: Graph A accurately represents the equation $-2x - 16y = -8$. The line passes through the points $(0, \frac{1}{2})$ and $(4, 0)$, and the equation is satisfied for both points.

Q: Why does Graph B not accurately represent the equation $-2x - 16y = -8$?

A: Graph B does not accurately represent the equation $-2x - 16y = -8$ because the point $(0, -\frac{1}{2})$ is not on the line.

Q: How do I determine which graph accurately represents a linear equation?

A: To determine which graph accurately represents a linear equation, you can substitute the coordinates of the points on each graph into the equation and see which one satisfies the equation.

Q: What is the slope of the line represented by Graph A?

A: The slope of the line represented by Graph A is $\frac{1}{4}$.

Q: What is the y-intercept of the line represented by Graph A?

A: The y-intercept of the line represented by Graph A is $\frac{1}{2}$.

Q: What is the slope of the line represented by Graph B?

A: The slope of the line represented by Graph B is $-\frac{1}{8}$.

Q: What is the y-intercept of the line represented by Graph B?

A: The y-intercept of the line represented by Graph B is $-\frac{1}{2}$.

Q: Can I use Graph B to represent the equation $-2x - 16y = -8$?

A: No, you cannot use Graph B to represent the equation $-2x - 16y = -8$ because it does not accurately represent the equation.

Q: Can I use Graph A to represent the equation $-2x - 16y = -8$?

A: Yes, you can use Graph A to represent the equation $-2x - 16y = -8$ because it accurately represents the equation.

Conclusion

In this article, we have discussed how to choose the best graph to represent a linear equation. We have examined two possible graphs, A and B, and determined which one accurately represents the equation $-2x - 16y = -8$. We have also answered some frequently asked questions about linear equations and graphing.