From The Graph, Calculate $E=\frac{3y-2x}{6}$:A. 10 B. 20 C. 30 D. 15 E. 40

Introduction

In this article, we will be solving for the value of E using a given equation and a graph. The equation provided is $E=\frac{3y-2x}{6}$, and we will use the graph to find the values of x and y that satisfy this equation. We will then substitute these values into the equation to solve for E.

Understanding the Equation

The equation provided is a linear equation in two variables, x and y. It is in the form of $E=\frac{3y-2x}{6}$, where E is the dependent variable and x and y are the independent variables. To solve for E, we need to find the values of x and y that satisfy this equation.

Graph Analysis

The graph provided shows a line with a positive slope. The line intersects the y-axis at a point (0, 5) and the x-axis at a point (-2, 0). We can use this information to find the values of x and y that satisfy the equation.

Finding the Values of x and y

To find the values of x and y that satisfy the equation, we can use the point (0, 5) that lies on the line. Substituting x = 0 and y = 5 into the equation, we get:

$$E=\frac{3(5)-2(0)}{6}$$

Simplifying the equation, we get:

$$E=\frac{15}{6}$$

Solving for E

Now that we have the value of E, we can solve for it. Dividing both sides of the equation by 6, we get:

$$E=2.5$$

However, this is not one of the answer choices provided. Let's try another point on the line. Substituting x = -2 and y = 0 into the equation, we get:

$$E=\frac{3(0)-2(-2)}{6}$$

Simplifying the equation, we get:

$$E=\frac{4}{6}$$

Simplifying the Equation

To simplify the equation, we can divide both sides by 6:

$$E=\frac{2}{3}$$

Conclusion

Q: What is the equation provided in the problem?

A: The equation provided is $E=\frac{3y-2x}{6}$, where E is the dependent variable and x and y are the independent variables.

Q: What is the graph used for in the problem?

A: The graph is used to find the values of x and y that satisfy the equation. By analyzing the graph, we can determine the points that lie on the line and substitute these values into the equation to solve for E.

Q: How do I find the values of x and y that satisfy the equation?

A: To find the values of x and y that satisfy the equation, you can use the points that lie on the line. You can substitute these values into the equation and solve for E.

Q: What if I don't have a graph to analyze?

A: If you don't have a graph to analyze, you can use other methods to find the values of x and y that satisfy the equation. For example, you can use algebraic methods or numerical methods to solve for E.

Q: Can I use any point on the line to solve for E?

A: No, you cannot use any point on the line to solve for E. You need to choose a point that lies on the line and satisfies the equation.

Q: How do I simplify the equation to solve for E?

A: To simplify the equation, you can divide both sides by the denominator (6) to isolate E.

Q: What is the final answer to the problem?

A: The final answer to the problem is $\boxed{\frac{2}{3}}$.

Q: Can I use a calculator to solve for E?

A: Yes, you can use a calculator to solve for E. However, make sure to enter the values correctly and follow the order of operations.

Q: What if I get a different answer than $\boxed{\frac{2}{3}}$?

A: If you get a different answer than $\boxed{\frac{2}{3}}$, it may be due to a calculation error or an incorrect assumption. Double-check your work and make sure to follow the correct steps to solve for E.

Q: Can I use this method to solve other equations?

A: Yes, you can use this method to solve other equations that involve linear relationships between variables. However, make sure to adjust the equation and the graph accordingly to solve for the desired variable.

Q: Where can I find more information on solving equations?

A: You can find more information on solving equations in algebra textbooks, online resources, or by consulting with a math tutor or instructor.