What Is The $y$-intercept Of $y=\frac{2}{3} X+2$?Write Your Answer As A Coordinate Pair.
Introduction
In mathematics, the $y$-intercept is a crucial concept in graphing linear equations. It represents the point at which the line intersects the $y$-axis. To find the $y$-intercept, we need to understand the equation of a line in slope-intercept form, which is given by $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.
Understanding the Equation
The given equation is $y = \frac{2}{3} x + 2$. In this equation, the slope $m$ is $\frac{2}{3}$, and the $y$-intercept $b$ is $2$. The slope represents the rate of change of the line, while the $y$-intercept represents the point at which the line intersects the $y$-axis.
Finding the $y$-Intercept
To find the $y$-intercept, we need to understand that the $y$-intercept occurs when the value of $x$ is equal to $0$. This is because the $y$-axis is the vertical line that passes through the point $(0, 0)$. Therefore, to find the $y$-intercept, we need to substitute $x = 0$ into the equation.
Substituting $x = 0$
Substituting $x = 0$ into the equation $y = \frac{2}{3} x + 2$, we get:
Simplifying the Equation
Simplifying the equation, we get:
Writing the Answer as a Coordinate Pair
The $y$-intercept is the point at which the line intersects the $y$-axis. Therefore, the $y$-intercept can be written as a coordinate pair $(0, y)$. In this case, the $y$-intercept is $(0, 2)$.
Conclusion
In conclusion, the $y$-intercept of the equation $y = \frac{2}{3} x + 2$ is $(0, 2)$. This represents the point at which the line intersects the $y$-axis. Understanding the concept of the $y$-intercept is crucial in graphing linear equations and is an essential concept in mathematics.
Frequently Asked Questions
- What is the $y$-intercept of a linear equation?
- How do you find the $y$-intercept of a linear equation?
- What is the equation of a line in slope-intercept form?
- What is the slope-intercept form of a linear equation?
Answering the FAQs
- The $y$-intercept of a linear equation is the point at which the line intersects the $y$-axis.
- To find the $y$-intercept of a linear equation, you need to substitute $x = 0$ into the equation.
- The equation of a line in slope-intercept form is given by $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.
- The slope-intercept form of a linear equation is given by $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.
Additional Resources
- Khan Academy: Linear Equations
- Mathway: Linear Equations
- Wolfram Alpha: Linear Equations
Final Thoughts
In conclusion, the $y$-intercept of the equation $y = \frac{2}{3} x + 2$ is $(0, 2)$. This represents the point at which the line intersects the $y$-axis. Understanding the concept of the $y$-intercept is crucial in graphing linear equations and is an essential concept in mathematics.
Introduction
In our previous article, we discussed the concept of the $y$-intercept of a linear equation. We learned that the $y$-intercept is the point at which the line intersects the $y$-axis and is represented by the equation $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. In this article, we will answer some frequently asked questions about the $y$-intercept of a linear equation.
Q&A
Q: What is the $y$-intercept of a linear equation?
A: The $y$-intercept of a linear equation is the point at which the line intersects the $y$-axis. It is represented by the equation $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.
Q: How do you 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. This will give you the value of $y$, which is the $y$-intercept.
Q: What is the equation of a line in slope-intercept form?
A: The equation of a line in slope-intercept form is given by $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.
Q: What is the slope-intercept form of a linear equation?
A: The slope-intercept form of a linear equation is given by $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.
Q: How do you graph a linear equation?
A: To graph a linear equation, you need to find the $y$-intercept and the slope. The $y$-intercept is the point at which the line intersects the $y$-axis, and the slope is the rate of change of the line. You can use a graphing calculator or a coordinate plane to graph the line.
Q: What is the difference between the $y$-intercept and the $x$-intercept?
A: The $y$-intercept is the point at which the line intersects the $y$-axis, while the $x$-intercept is the point at which the line intersects the $x$-axis. The $y$-intercept is represented by the equation $y = mx + b$, while the $x$-intercept is represented by the equation $x = my + b$.
Q: How do you find the $x$-intercept of a linear equation?
A: To find the $x$-intercept of a linear equation, you need to substitute $y = 0$ into the equation. This will give you the value of $x$, which is the $x$-intercept.
Conclusion
In conclusion, the $y$-intercept of a linear equation is the point at which the line intersects the $y$-axis. It is represented by the equation $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. Understanding the concept of the $y$-intercept is crucial in graphing linear equations and is an essential concept in mathematics.
Frequently Asked Questions
- What is the $y$-intercept of a linear equation?
- How do you find the $y$-intercept of a linear equation?
- What is the equation of a line in slope-intercept form?
- What is the slope-intercept form of a linear equation?
- How do you graph a linear equation?
- What is the difference between the $y$-intercept and the $x$-intercept?
- How do you find the $x$-intercept of a linear equation?
Answering the FAQs
- The $y$-intercept of a linear equation is the point at which the line intersects the $y$-axis.
- To find the $y$-intercept of a linear equation, you need to substitute $x = 0$ into the equation.
- The equation of a line in slope-intercept form is given by $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.
- The slope-intercept form of a linear equation is given by $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.
- To graph a linear equation, you need to find the $y$-intercept and the slope.
- The $y$-intercept is the point at which the line intersects the $y$-axis, while the $x$-intercept is the point at which the line intersects the $x$-axis.
- To find the $x$-intercept of a linear equation, you need to substitute $y = 0$ into the equation.
Additional Resources
- Khan Academy: Linear Equations
- Mathway: Linear Equations
- Wolfram Alpha: Linear Equations
Final Thoughts
In conclusion, the $y$-intercept of a linear equation is the point at which the line intersects the $y$-axis. It is represented by the equation $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. Understanding the concept of the $y$-intercept is crucial in graphing linear equations and is an essential concept in mathematics.