Rewrite The Following Equation In Slope-intercept Form: − 8 X − 13 Y − 10 = 0 -8x - 13y - 10 = 0 − 8 X − 13 Y − 10 = 0 Write Your Answer Using Integers, Proper Fractions, And Improper Fractions In Simplest Form. □ \square □

Introduction

In mathematics, the slope-intercept form of a linear equation is a way to express the equation in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. This form is useful for graphing lines and understanding their properties. In this article, we will rewrite the given equation in slope-intercept form and provide the solution using integers, proper fractions, and improper fractions in simplest form.

The Given Equation

The given equation is:

$$-8x - 13y - 10 = 0$$

Step 1: Add 10 to Both Sides

To isolate the term with y, we need to add 10 to both sides of the equation. This will give us:

$$-8x - 13y = 10$$

Step 2: Add 8x to Both Sides

Next, we need to add 8x to both sides of the equation to get all the x terms on one side. This will give us:

$$-13y = 10 + 8x$$

Step 3: Divide Both Sides by -13

Now, we need to divide both sides of the equation by -13 to solve for y. This will give us:

$$y = -\frac{10 + 8x}{13}$$

Simplifying the Equation

We can simplify the equation by combining the terms in the numerator:

$$y = -\frac{10}{13} - \frac{8x}{13}$$

Slope-Intercept Form

The equation is now in slope-intercept form, where m is the slope and b is the y-intercept:

$$y = -\frac{8}{13}x - \frac{10}{13}$$

Conclusion

In this article, we rewrote the given equation in slope-intercept form and provided the solution using integers, proper fractions, and improper fractions in simplest form. The final equation is:

$$y = -\frac{8}{13}x - \frac{10}{13}$$

This form is useful for graphing lines and understanding their properties.

Key Takeaways

• The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
• To rewrite an equation in slope-intercept form, we need to isolate the term with y and then divide both sides by the coefficient of y.
• The final equation in slope-intercept form is y = -\frac{8}{13}x - \frac{10}{13}.

Common Mistakes to Avoid

• Not isolating the term with y before dividing both sides by the coefficient of y.
• Not simplifying the equation after dividing both sides by the coefficient of y.

Real-World Applications

• Graphing lines and understanding their properties.
• Solving systems of linear equations.
• Finding the equation of a line given two points.

Practice Problems

• Rewrite the equation 2x + 5y - 3 = 0 in slope-intercept form.
• Rewrite the equation x - 2y + 1 = 0 in slope-intercept form.

Conclusion

In this article, we rewrote the given equation in slope-intercept form and provided the solution using integers, proper fractions, and improper fractions in simplest form. The final equation is:

$$y = -\frac{8}{13}x - \frac{10}{13}$$

Introduction

In our previous article, we rewrote the equation -8x - 13y - 10 = 0 in slope-intercept form and provided the solution using integers, proper fractions, and improper fractions in simplest form. In this article, we will answer some frequently asked questions about solving linear equations in slope-intercept form.

Q: What is the slope-intercept form of a linear equation?

A: The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept.

Q: How do I rewrite an equation in slope-intercept form?

A: To rewrite an equation in slope-intercept form, you need to isolate the term with y and then divide both sides by the coefficient of y.

Q: What is the coefficient of y?

A: The coefficient of y is the number that is multiplied by y in the equation. For example, in the equation -8x - 13y - 10 = 0, the coefficient of y is -13.

Q: How do I simplify the equation after dividing both sides by the coefficient of y?

A: To simplify the equation, you can combine the terms in the numerator and then simplify the fraction.

Q: What is the final equation in slope-intercept form?

A: The final equation in slope-intercept form is y = -\frac{8}{13}x - \frac{10}{13}.

Q: How do I graph a line in slope-intercept form?

A: To graph a line in slope-intercept form, you can use the slope (m) and the y-intercept (b) to find two points on the line. Then, you can draw a line through those two points.

Q: What are some common mistakes to avoid when rewriting an equation in slope-intercept form?

A: Some common mistakes to avoid when rewriting an equation in slope-intercept form include not isolating the term with y before dividing both sides by the coefficient of y, and not simplifying the equation after dividing both sides by the coefficient of y.

Q: What are some real-world applications of solving linear equations in slope-intercept form?

A: Some real-world applications of solving linear equations in slope-intercept form include graphing lines and understanding their properties, solving systems of linear equations, and finding the equation of a line given two points.

Q: How do I practice solving linear equations in slope-intercept form?

A: You can practice solving linear equations in slope-intercept form by rewriting equations in slope-intercept form and then checking your answers by graphing the line.

Q: What are some tips for solving linear equations in slope-intercept form?

A: Some tips for solving linear equations in slope-intercept form include using a calculator to simplify fractions, and checking your answers by graphing the line.

Conclusion

In this article, we answered some frequently asked questions about solving linear equations in slope-intercept form. We hope that this article has been helpful in understanding how to rewrite equations in slope-intercept form and solve them using integers, proper fractions, and improper fractions in simplest form.

Practice Problems

• Rewrite the equation 2x + 5y - 3 = 0 in slope-intercept form.
• Rewrite the equation x - 2y + 1 = 0 in slope-intercept form.
• Graph the line y = -\frac{8}{13}x - \frac{10}{13}.

Common Mistakes to Avoid

• Not isolating the term with y before dividing both sides by the coefficient of y.
• Not simplifying the equation after dividing both sides by the coefficient of y.

Real-World Applications

• Graphing lines and understanding their properties.
• Solving systems of linear equations.
• Finding the equation of a line given two points.

Conclusion

In this article, we answered some frequently asked questions about solving linear equations in slope-intercept form. We hope that this article has been helpful in understanding how to rewrite equations in slope-intercept form and solve them using integers, proper fractions, and improper fractions in simplest form.