Becca Graphs The Equations Y = − 3 ( X − 1 Y=-3(x-1 Y = − 3 ( X − 1 ] And Y = X − 5 Y=x-5 Y = X − 5 To Solve The Equation − 3 ( X − 1 ) = X − 5 -3(x-1)=x-5 − 3 ( X − 1 ) = X − 5 . What Are The Solution(s) Of − 3 ( X − 1 ) = X − 5 -3(x-1)=x-5 − 3 ( X − 1 ) = X − 5 ?

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Introduction

Graphing equations is a powerful tool in mathematics that allows us to visualize and solve equations in a more intuitive way. In this article, we will explore how Becca uses graphing to solve the equation $-3(x-1)=x-5$. We will delve into the world of linear equations, graphing, and problem-solving, and provide a step-by-step guide on how to solve the equation using graphing.

Understanding the Equation

The equation $-3(x-1)=x-5$ is a linear equation that can be solved using various methods, including graphing. To begin, let's break down the equation and understand its components. The equation consists of two terms: $-3(x-1)$ and $x-5$. The first term is a linear expression that can be simplified to $-3x+3$, while the second term is a linear expression that remains as $x-5$.

Graphing the Equations

To solve the equation $-3(x-1)=x-5$, Becca graphs the two equations $y=-3(x-1)$ and $y=x-5$ on the same coordinate plane. The first equation, $y=-3(x-1)$, can be rewritten as $y=-3x+3$, which is a linear equation with a slope of $-3$ and a y-intercept of $3$. The second equation, $y=x-5$, is also a linear equation with a slope of $1$ and a y-intercept of $-5$.

Finding the Solution

When Becca graphs the two equations, she notices that they intersect at a single point. This point represents the solution to the equation $-3(x-1)=x-5$. To find the solution, Becca can use the point of intersection as the solution to the equation.

Solving the Equation Algebraically

In addition to graphing, Becca can also solve the equation $-3(x-1)=x-5$ algebraically. To do this, she can start by simplifying the equation and isolating the variable $x$. The equation can be rewritten as $-3x+3=x-5$, which can be further simplified to $-4x=-8$. Dividing both sides by $-4$, Becca finds that $x=2$.

Conclusion

In this article, we explored how Becca uses graphing to solve the equation $-3(x-1)=x-5$. We broke down the equation, graphed the two equations, and found the solution using the point of intersection. We also solved the equation algebraically and found that the solution is $x=2$. Graphing is a powerful tool in mathematics that allows us to visualize and solve equations in a more intuitive way. By combining graphing with algebraic techniques, we can solve equations and gain a deeper understanding of mathematical concepts.

Step-by-Step Guide to Solving the Equation

Step 1: Graph the Two Equations

To solve the equation $-3(x-1)=x-5$, Becca graphs the two equations $y=-3(x-1)$ and $y=x-5$ on the same coordinate plane.

Step 2: Find the Point of Intersection

Becca finds the point of intersection between the two graphs, which represents the solution to the equation.

Step 3: Solve the Equation Algebraically

Becca can also solve the equation $-3(x-1)=x-5$ algebraically by simplifying the equation and isolating the variable $x$.

Step 4: Verify the Solution

Becca can verify the solution by plugging the value of $x$ back into the original equation and checking if it is true.

Frequently Asked Questions

Q: What is the solution to the equation $-3(x-1)=x-5$?

A: The solution to the equation $-3(x-1)=x-5$ is $x=2$.

Q: How can I graph the two equations?

A: To graph the two equations, you can use a graphing calculator or graph paper. Plot the two equations on the same coordinate plane and find the point of intersection.

Q: Can I solve the equation algebraically?

A: Yes, you can solve the equation $-3(x-1)=x-5$ algebraically by simplifying the equation and isolating the variable $x$.

Q: How can I verify the solution?

A: You can verify the solution by plugging the value of $x$ back into the original equation and checking if it is true.

Conclusion

In conclusion, graphing is a powerful tool in mathematics that allows us to visualize and solve equations in a more intuitive way. By combining graphing with algebraic techniques, we can solve equations and gain a deeper understanding of mathematical concepts. In this article, we explored how Becca uses graphing to solve the equation $-3(x-1)=x-5$ and provided a step-by-step guide on how to solve the equation using graphing.

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Introduction

In our previous article, we explored how Becca uses graphing to solve the equation $-3(x-1)=x-5$. We broke down the equation, graphed the two equations, and found the solution using the point of intersection. We also solved the equation algebraically and found that the solution is $x=2$. In this article, we will provide a Q&A section to answer some of the most frequently asked questions about graphing and solving equations.

Q&A

Q: What is the difference between graphing and solving equations algebraically?

A: Graphing and solving equations algebraically are two different methods of solving equations. Graphing involves visualizing the equation on a coordinate plane and finding the point of intersection, while solving equations algebraically involves simplifying the equation and isolating the variable.

Q: How can I graph the two equations?

A: To graph the two equations, you can use a graphing calculator or graph paper. Plot the two equations on the same coordinate plane and find the point of intersection.

Q: Can I solve the equation $-3(x-1)=x-5$ algebraically?

A: Yes, you can solve the equation $-3(x-1)=x-5$ algebraically by simplifying the equation and isolating the variable $x$.

Q: How can I verify the solution?

A: You can verify the solution by plugging the value of $x$ back into the original equation and checking if it is true.

Q: What is the point of intersection?

A: The point of intersection is the point where the two graphs meet. This point represents the solution to the equation.

Q: Can I use graphing to solve systems of equations?

A: Yes, you can use graphing to solve systems of equations. By graphing the two equations on the same coordinate plane, you can find the point of intersection, which represents the solution to the system of equations.

Q: How can I use graphing to solve quadratic equations?

A: You can use graphing to solve quadratic equations by graphing the quadratic function and finding the x-intercepts. The x-intercepts represent the solutions to the quadratic equation.

Q: Can I use graphing to solve polynomial equations?

A: Yes, you can use graphing to solve polynomial equations by graphing the polynomial function and finding the x-intercepts. The x-intercepts represent the solutions to the polynomial equation.

Q: How can I use graphing to solve rational equations?

A: You can use graphing to solve rational equations by graphing the rational function and finding the x-intercepts. The x-intercepts represent the solutions to the rational equation.

Conclusion

In conclusion, graphing is a powerful tool in mathematics that allows us to visualize and solve equations in a more intuitive way. By combining graphing with algebraic techniques, we can solve equations and gain a deeper understanding of mathematical concepts. In this article, we provided a Q&A section to answer some of the most frequently asked questions about graphing and solving equations.

Additional Resources

• Graphing Calculator: A graphing calculator is a tool that allows you to graph functions and find the point of intersection.
• Graph Paper: Graph paper is a tool that allows you to graph functions and find the point of intersection.
• Algebraic Techniques: Algebraic techniques involve simplifying the equation and isolating the variable.
• Systems of Equations: A system of equations is a set of two or more equations that are solved simultaneously.
• Quadratic Equations: A quadratic equation is a polynomial equation of degree two.
• Polynomial Equations: A polynomial equation is a polynomial equation of degree three or higher.
• Rational Equations: A rational equation is a polynomial equation that contains a rational expression.

Frequently Asked Questions

Q: What is the solution to the equation $-3(x-1)=x-5$?

A: The solution to the equation $-3(x-1)=x-5$ is $x=2$.

Q: How can I graph the two equations?

A: To graph the two equations, you can use a graphing calculator or graph paper. Plot the two equations on the same coordinate plane and find the point of intersection.

Q: Can I solve the equation $-3(x-1)=x-5$ algebraically?

A: Yes, you can solve the equation $-3(x-1)=x-5$ algebraically by simplifying the equation and isolating the variable $x$.

Q: How can I verify the solution?

A: You can verify the solution by plugging the value of $x$ back into the original equation and checking if it is true.

Conclusion

In conclusion, graphing is a powerful tool in mathematics that allows us to visualize and solve equations in a more intuitive way. By combining graphing with algebraic techniques, we can solve equations and gain a deeper understanding of mathematical concepts. In this article, we provided a Q&A section to answer some of the most frequently asked questions about graphing and solving equations.