Rewrite The Following Equation In Slope-intercept Form.$10x - 15y = 7$

Introduction

In mathematics, the slope-intercept form of a linear equation is a fundamental concept that helps us understand the relationship between the variables in an equation. The slope-intercept form is written as y = mx + b, where m is the slope of the line and b is the y-intercept. In this article, we will learn how to rewrite the given equation in slope-intercept form.

Understanding the Given Equation

The given equation is $10x - 15y = 7$. To rewrite this equation in slope-intercept form, we need to isolate the variable y. The first step is to get all the terms involving y on one side of the equation.

Step 1: Get all the terms involving y on one side of the equation

To do this, we can add 15y to both sides of the equation. This will give us:

$10x - 15y + 15y = 7 + 15y$

Simplifying the equation, we get:

$10x = 7 + 15y$

Step 2: Isolate the variable y

Now, we need to isolate the variable y. To do this, we can subtract 7 from both sides of the equation. This will give us:

$10x - 7 = 15y$

Next, we can divide both sides of the equation by 15. This will give us:

$\frac{10x - 7}{15} = y$

Step 3: Rewrite the equation in slope-intercept form

Now that we have isolated the variable y, we can rewrite the equation in slope-intercept form. To do this, we can simplify the equation by dividing the numerator by 15. This will give us:

$y = \frac{2}{3}x - \frac{7}{15}$

Conclusion

In this article, we learned how to rewrite the given equation in slope-intercept form. We started by getting all the terms involving y on one side of the equation, then isolated the variable y, and finally rewrote the equation in slope-intercept form. The final answer is $y = \frac{2}{3}x - \frac{7}{15}$.

Key Takeaways

• The slope-intercept form of a linear equation is written as y = mx + b, where m is the slope of the line and b is the y-intercept.
• To rewrite an equation in slope-intercept form, we need to isolate the variable y.
• We can get all the terms involving y on one side of the equation by adding or subtracting the same value from both sides.
• We can isolate the variable y by dividing both sides of the equation by a non-zero value.

Practice Problems

1. Rewrite the equation $5x - 2y = 3$ in slope-intercept form.
2. Rewrite the equation $2x + 3y = 5$ in slope-intercept form.
3. Rewrite the equation $x - 4y = 2$ in slope-intercept form.

Solutions

1. $y = \frac{5}{2}x - \frac{3}{2}$
2. $y = -\frac{2}{3}x + \frac{5}{3}$
3. $y = \frac{1}{4}x - \frac{1}{2}$
   Frequently Asked Questions: Slope-Intercept Form =====================================================

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

A: The slope-intercept form of a linear equation is written as 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 variable y. You can do this by getting all the terms involving y on one side of the equation, then isolating the variable y by dividing both sides of the equation by a non-zero value.

Q: What is the slope of a line in slope-intercept form?

A: The slope of a line in slope-intercept form is the coefficient of the x term, which is represented by the variable m.

Q: What is the y-intercept of a line in slope-intercept form?

A: The y-intercept of a line in slope-intercept form is the constant term, which is represented by the variable b.

Q: How do I find the slope and y-intercept of a line in slope-intercept form?

A: To find the slope and y-intercept of a line in slope-intercept form, you can look at the equation and identify the values of m and b.

Q: Can I have a negative slope in slope-intercept form?

A: Yes, you can have a negative slope in slope-intercept form. For example, the equation y = -2x + 3 has a negative slope.

Q: Can I have a fractional slope in slope-intercept form?

A: Yes, you can have a fractional slope in slope-intercept form. For example, the equation y = (1/2)x + 2 has a fractional slope.

Q: Can I have a zero slope in slope-intercept form?

A: Yes, you can have a zero slope in slope-intercept form. For example, the equation y = 0x + 2 has a zero slope.

Q: Can I have a vertical line in slope-intercept form?

A: No, you cannot have a vertical line in slope-intercept form. A vertical line has an undefined slope, which cannot be represented in slope-intercept form.

Q: Can I have a horizontal line in slope-intercept form?

A: Yes, you can have a horizontal line in slope-intercept form. For example, the equation y = 2 has a horizontal line with a slope of 0.

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 and y-intercept to find two points on the line, then draw a line through those points.

Q: Can I use slope-intercept form to find the equation of a line?

A: Yes, you can use slope-intercept form to find the equation of a line. You can use the slope and y-intercept to write the equation in slope-intercept form.

Q: Can I use slope-intercept form to find the slope and y-intercept of a line?

A: Yes, you can use slope-intercept form to find the slope and y-intercept of a line. You can look at the equation and identify the values of m and b.

Q: Is slope-intercept form the only way to write a linear equation?

A: No, slope-intercept form is not the only way to write a linear equation. You can also write a linear equation in standard form, which is written as ax + by = c.

Q: When should I use slope-intercept form?

A: You should use slope-intercept form when you need to find the slope and y-intercept of a line, or when you need to graph a line.

Q: When should I use standard form?

A: You should use standard form when you need to find the equation of a line in a specific format, or when you need to perform operations on the equation.

Conclusion

In this article, we answered some frequently asked questions about slope-intercept form. We covered topics such as how to rewrite an equation in slope-intercept form, how to find the slope and y-intercept of a line, and when to use slope-intercept form. We hope this article has been helpful in answering your questions about slope-intercept form.