Find The \[$ Y \$\]-intercept Of The Line \[$ Y = -23x \$\].Write Your Answer As An Integer Or As A Simplified Proper Or Improper Fraction, Not As An Ordered Pair.\[$\square\$\]
Understanding the y-intercept
The y-intercept of a linear equation is the point at which the line intersects the y-axis. It is the value of y when x is equal to zero. In other words, it is the value of y that the line reaches when it crosses the y-axis.
The Equation y = -23x
The given equation is y = -23x. This is a linear equation in the slope-intercept form, where the slope is -23 and the y-intercept is the value we are trying to find.
Finding the y-intercept
To find the y-intercept, we need to substitute x = 0 into the equation and solve for y.
y = -23x y = -23(0) y = 0
The y-intercept is 0
Therefore, the y-intercept of the line y = -23x is 0.
Why is the y-intercept 0?
The y-intercept is 0 because the equation y = -23x is a linear equation with a negative slope. When x is equal to 0, the value of y is also equal to 0. This is because the line passes through the origin (0, 0) and has a negative slope, which means that it decreases as x increases.
Conclusion
In conclusion, the y-intercept of the line y = -23x is 0. This is because the equation is a linear equation with a negative slope, and when x is equal to 0, the value of y is also equal to 0.
Example Questions
- Find the y-intercept of the line y = 2x.
- Find the y-intercept of the line y = -x.
- Find the y-intercept of the line y = 3x + 2.
Answer Key
- The y-intercept of the line y = 2x is 0.
- The y-intercept of the line y = -x is 0.
- The y-intercept of the line y = 3x + 2 is -2.
Tips and Tricks
- To find the y-intercept of a linear equation, substitute x = 0 into the equation and solve for y.
- The y-intercept is the value of y when x is equal to 0.
- The y-intercept is the point at which the line intersects the y-axis.
Common Mistakes
- Not substituting x = 0 into the equation.
- Not solving for y when x is equal to 0.
- Not understanding that the y-intercept is the value of y when x is equal to 0.
Real-World Applications
- Finding the y-intercept of a linear equation is important in many real-world applications, such as physics, engineering, and economics.
- The y-intercept can be used to model real-world situations, such as the cost of producing a product or the demand for a product.
- The y-intercept can be used to make predictions about future events, such as the price of a stock or the demand for a product.
Conclusion
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 the value of y when x is equal to zero.
Q: How do I find the y-intercept of a linear equation?
A: To find the y-intercept, substitute x = 0 into the equation and solve for y.
Q: What is the equation y = -23x?
A: The equation y = -23x is a linear equation in the slope-intercept form, where the slope is -23 and the y-intercept is the value we are trying to find.
Q: What is the y-intercept of the line y = -23x?
A: The y-intercept of the line y = -23x is 0.
Q: Why is the y-intercept 0?
A: The y-intercept is 0 because the equation y = -23x is a linear equation with a negative slope. When x is equal to 0, the value of y is also equal to 0.
Q: Can you give an example of finding the y-intercept of a linear equation?
A: Yes, let's find the y-intercept of the line y = 2x.
To find the y-intercept, substitute x = 0 into the equation and solve for y.
y = 2x y = 2(0) y = 0
Therefore, the y-intercept of the line y = 2x is 0.
Q: What are some common mistakes to avoid when finding the y-intercept of a linear equation?
A: Some common mistakes to avoid when finding the y-intercept of a linear equation include:
- Not substituting x = 0 into the equation.
- Not solving for y when x is equal to 0.
- Not understanding that the y-intercept is the value of y when x is equal to 0.
Q: What are some real-world applications of finding the y-intercept of a linear equation?
A: Some real-world applications of finding the y-intercept of a linear equation include:
- Modeling the cost of producing a product.
- Modeling the demand for a product.
- Making predictions about future events, such as the price of a stock or the demand for a product.
Q: Can you give some tips and tricks for finding the y-intercept of a linear equation?
A: Yes, here are some tips and tricks for finding the y-intercept of a linear equation:
- To find the y-intercept, substitute x = 0 into the equation and solve for y.
- The y-intercept is the value of y when x is equal to 0.
- The y-intercept is the point at which the line intersects the y-axis.
Q: What is the difference between the y-intercept and the x-intercept of a linear equation?
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.
Q: Can you give an example of finding the x-intercept of a linear equation?
A: Yes, let's find the x-intercept of the line y = 2x.
To find the x-intercept, substitute y = 0 into the equation and solve for x.
y = 2x 0 = 2x x = 0
Therefore, the x-intercept of the line y = 2x is 0.
Q: What are some common mistakes to avoid when finding the x-intercept of a linear equation?
A: Some common mistakes to avoid when finding the x-intercept of a linear equation include:
- Not substituting y = 0 into the equation.
- Not solving for x when y is equal to 0.
- Not understanding that the x-intercept is the value of x when y is equal to 0.
Q: What are some real-world applications of finding the x-intercept of a linear equation?
A: Some real-world applications of finding the x-intercept of a linear equation include:
- Modeling the cost of producing a product.
- Modeling the demand for a product.
- Making predictions about future events, such as the price of a stock or the demand for a product.
Q: Can you give some tips and tricks for finding the x-intercept of a linear equation?
A: Yes, here are some tips and tricks for finding the x-intercept of a linear equation:
- To find the x-intercept, substitute y = 0 into the equation and solve for x.
- The x-intercept is the value of x when y is equal to 0.
- The x-intercept is the point at which the line intersects the x-axis.