What Is The Slope And The { Y $}$-intercept Of The Equation { 9+\frac{27}{2} X=-\frac{3}{2} Y $}$?Write The { Y $}$-intercept As An Ordered Pair.
Introduction
When dealing with linear equations, it's essential to understand the concepts of slope and y-intercept. The slope represents the rate of change of the equation, while the y-intercept is the point where the line intersects the y-axis. In this article, we will explore how to find the slope and y-intercept of the given equation 9+\frac{27}{2} x=-\frac{3}{2} y.
Understanding the Equation
The given equation is 9+\frac{27}{2} x=-\frac{3}{2} y. To find the slope and y-intercept, we need to rewrite the equation in the standard form, which is y = mx + b, where m is the slope and b is the y-intercept.
Rearranging the Equation
To rewrite the equation in the standard form, we need to isolate y on one side of the equation. We can start by multiplying both sides of the equation by -2 to eliminate the fraction.
-2(9 + \frac{27}{2}x) = -2(-\frac{3}{2}y)
This simplifies to:
-18 - 27x = 3y
Isolating y
Now, we can isolate y by dividing both sides of the equation by 3.
\frac{-18 - 27x}{3} = y
This simplifies to:
y = -6 - 9x
Finding the Slope
The slope of the equation is the coefficient of x, which is -9.
Finding the y-intercept
The y-intercept is the point where the line intersects the y-axis, which is when x = 0. To find the y-intercept, we can substitute x = 0 into the equation.
y = -6 - 9(0)
This simplifies to:
y = -6
Writing the y-intercept as an Ordered Pair
The y-intercept is the point (0, -6).
Conclusion
In conclusion, the slope of the equation 9+\frac{27}{2} x=-\frac{3}{2} y is -9, and the y-intercept is (0, -6). Understanding the concepts of slope and y-intercept is essential in linear algebra and is used in various applications such as physics, engineering, and economics.
Frequently Asked Questions
- What is the slope of the equation 9+\frac{27}{2} x=-\frac{3}{2} y?
- The slope of the equation is -9.
- What is the y-intercept of the equation 9+\frac{27}{2} x=-\frac{3}{2} y?
- The y-intercept of the equation is (0, -6).
- How do I find the slope and y-intercept of a linear equation?
- To find the slope and y-intercept of a linear equation, you need to rewrite the equation in the standard form, which is y = mx + b, where m is the slope and b is the y-intercept.
References
Further Reading
Introduction
In our previous article, we explored how to find the slope and y-intercept of the equation 9+\frac{27}{2} x=-\frac{3}{2} y. In this article, we will answer some frequently asked questions related to the slope and y-intercept of a linear equation.
Q&A
Q: What is the slope of a linear equation?
A: The slope of a linear equation is the coefficient of x in the equation. It represents the rate of change of the equation.
Q: How do I find the slope of a linear equation?
A: To find the slope of a linear equation, you need to rewrite the equation in the standard form, which is y = mx + b, where m is the slope and b is the y-intercept.
Q: What is the y-intercept of a linear equation?
A: The y-intercept of a linear equation is the point where the line intersects the y-axis. It is the value of y when x = 0.
Q: How do I find the y-intercept of a linear equation?
A: To find the y-intercept of a linear equation, you need to substitute x = 0 into the equation and solve for y.
Q: What is the difference between the slope and y-intercept?
A: The slope represents the rate of change of the equation, while the y-intercept represents the point where the line intersects the y-axis.
Q: How do I use the slope and y-intercept to graph a linear equation?
A: To graph a linear equation, you need to use the slope and y-intercept to find two points on the line. Then, you can draw a line through the two points to graph the equation.
Q: Can the slope and y-intercept be negative?
A: Yes, the slope and y-intercept can be negative. A negative slope represents a downward-sloping line, while a negative y-intercept represents a line that intersects the y-axis below the origin.
Q: Can the slope and y-intercept be zero?
A: Yes, the slope and y-intercept can be zero. A slope of zero represents a horizontal line, while a y-intercept of zero represents a line that intersects the y-axis at the origin.
Conclusion
In conclusion, the slope and y-intercept are essential concepts in linear algebra. Understanding how to find and use the slope and y-intercept can help you graph and analyze linear equations.
Frequently Asked Questions
- What is the slope of a linear equation?
- How do I find the slope of a linear equation?
- What is the y-intercept of a linear equation?
- How do I find the y-intercept of a linear equation?
- What is the difference between the slope and y-intercept?
- How do I use the slope and y-intercept to graph a linear equation?
- Can the slope and y-intercept be negative?
- Can the slope and y-intercept be zero?