What Is $3y + 5x = -15$ Written In Slope-intercept Form?A. $y = \frac{5}{3}x + 5$B. $y = -\frac{5}{3}x - 5$C. $y = \frac{5}{3}x - 5$D. $y = -\frac{5}{3}x + 5$

What is $3y + 5x = -15$ written in slope-intercept form?

The slope-intercept form of a linear equation is a way to express the equation in the form $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept. This form is useful for graphing lines and understanding the relationship between the variables.

Converting the Given Equation to Slope-Intercept Form

To convert the given equation $3y + 5x = -15$ to slope-intercept form, we need to isolate the variable $y$ on one side of the equation. We can start by subtracting $5x$ from both sides of the equation:

$$3y = -5x - 15$$

Next, we can divide both sides of the equation by $3$ to isolate $y$:

$$y = \frac{-5x - 15}{3}$$

Simplifying the Equation

We can simplify the equation by combining the constants on the right-hand side:

$$y = \frac{-5x}{3} - 5$$

Writing the Equation in Slope-Intercept Form

Now that we have isolated $y$ on the left-hand side of the equation, we can write the equation in slope-intercept form:

$$y = -\frac{5}{3}x - 5$$

Comparing the Answer Choices

Let's compare our answer to the answer choices:

• A. $y = \frac{5}{3}x + 5$
• B. $y = -\frac{5}{3}x - 5$
• C. $y = \frac{5}{3}x - 5$
• D. $y = -\frac{5}{3}x + 5$

Our answer, $y = -\frac{5}{3}x - 5$, matches answer choice B.

Conclusion

In this article, we converted the given equation $3y + 5x = -15$ to slope-intercept form and found that the correct answer is $y = -\frac{5}{3}x - 5$. This form is useful for graphing lines and understanding the relationship between the variables.

Step-by-Step Solution

1. Subtract $5x$ from both sides of the equation: $3y = -5x - 15$
2. Divide both sides of the equation by $3$: $y = \frac{-5x - 15}{3}$
3. Simplify the equation: $y = \frac{-5x}{3} - 5$
4. Write the equation in slope-intercept form: $y = -\frac{5}{3}x - 5$

Key Concepts

• Slope-intercept form: $y = mx + b$
• Isolating the variable $y$ on one side of the equation
• Simplifying the equation by combining constants
• Writing the equation in slope-intercept form

Practice Problems

1. Convert the equation $2y + 3x = 10$ to slope-intercept form.
2. Convert the equation $4y - 2x = 12$ to slope-intercept form.
3. Convert the equation $y + 2x = 5$ to slope-intercept form.

Real-World Applications

• Graphing lines and understanding the relationship between variables
• Solving systems of linear equations
• Modeling real-world problems using linear equations

Common Mistakes

• Failing to isolate the variable $y$ on one side of the equation
• Not simplifying the equation by combining constants
• Writing the equation in the wrong form

Tips and Tricks

• Use the slope-intercept form to graph lines and understand the relationship between variables.
• Simplify the equation by combining constants to make it easier to work with.
• Check your answer by plugging it back into the original equation.
  Q&A: Converting Linear Equations to Slope-Intercept Form

The slope-intercept form of a linear equation is a way to express the equation in the form $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept. This form is useful for graphing lines and understanding the relationship between the variables.

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 convert a linear equation to slope-intercept form?

A: To convert a linear equation to slope-intercept form, you need to isolate the variable $y$ on one side of the equation. You can do this by subtracting the x-term from both sides of the equation and then dividing both sides by the coefficient of $y$.

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

A: The y-intercept in the slope-intercept form is the value of $b$, which is the point where the line intersects the y-axis.

Q: How do I find the slope in the slope-intercept form?

A: To find the slope in the slope-intercept form, you need to look at the coefficient of the x-term, which is $m$. This is the slope of the line.

Q: Can I use the slope-intercept form to graph a line?

A: Yes, you can use the slope-intercept form to graph a line. The slope-intercept form gives you the slope and y-intercept of the line, which you can use to graph the line.

Q: What are some common mistakes to avoid when converting a linear equation to slope-intercept form?

A: Some common mistakes to avoid when converting a linear equation to slope-intercept form include:

• Failing to isolate the variable $y$ on one side of the equation
• Not simplifying the equation by combining constants
• Writing the equation in the wrong form

Q: How do I check my answer when converting a linear equation to slope-intercept form?

A: To check your answer when converting a linear equation to slope-intercept form, you can plug it back into the original equation and see if it is true.

Q: Can I use the slope-intercept form to solve systems of linear equations?

A: Yes, you can use the slope-intercept form to solve systems of linear equations. By setting the two equations equal to each other, you can solve for the value of $x$ and then substitute that value into one of the original equations to solve for the value of $y$.

Q: What are some real-world applications of the slope-intercept form?

A: Some real-world applications of the slope-intercept form include:

• Graphing lines and understanding the relationship between variables
• Solving systems of linear equations
• Modeling real-world problems using linear equations

Practice Problems

1. Convert the equation $2y + 3x = 10$ to slope-intercept form.
2. Convert the equation $4y - 2x = 12$ to slope-intercept form.
3. Convert the equation $y + 2x = 5$ to slope-intercept form.

Real-World Applications

• Graphing lines and understanding the relationship between variables
• Solving systems of linear equations
• Modeling real-world problems using linear equations

Common Mistakes

• Failing to isolate the variable $y$ on one side of the equation
• Not simplifying the equation by combining constants
• Writing the equation in the wrong form

Tips and Tricks

• Use the slope-intercept form to graph lines and understand the relationship between variables.
• Simplify the equation by combining constants to make it easier to work with.
• Check your answer by plugging it back into the original equation.

Additional Resources

• Online resources for learning about the slope-intercept form
• Practice problems and worksheets for converting linear equations to slope-intercept form
• Real-world applications of the slope-intercept form