Intercepts of the Curve -7x3y15: Understanding X and Y Intercepts
Introduction to Intercepts
Understanding the intercepts of a curve, specifically the x and y intercepts, is crucial in analyzing the graphical representation of algebraic equations. The x-intercept and y-intercept provide valuable information about the points where the curve intersects with the coordinate axes. This article will explore how to find the x and y intercepts of the curve defined by the equation -7x3y 15.
What Are X and Y Intercepts?
The x-intercept of a curve is the point where the curve intersects the x-axis. It is the value of x when y equals zero. Conversely, the y-intercept is the point where the curve intersects the y-axis. It is the value of y when x equals zero.
How to Determine the X-Intercept
To find the x-intercept, we set y to zero and solve the equation for x.
Step 1: Set y0 in the equation
[-7x^3(0) 15]Simplifying the equation, we get:
[0 15]This step shows that the equation results in a contradiction, indicating that there are no x-intercepts for the curve defined by -7x3y 15. This is because the equation does not allow for any real value of x when y is set to zero.
How to Determine the Y-Intercept
To find the y-intercept, we set x to zero and solve the equation for y.
Step 1: Set x0 in the equation
[-7(0)^3y 15]Simplifying the equation, we get:
[0y 15]Dividing both sides by 0 would result in an undefined value, indicating a contradiction. However, we can solve for y as follows:
Since 0y 15, this is not possible unless y is undefined or infinite. Instead, we can interpret this as y being undefined or tending towards infinity. Therefore, the y-intercept is not a point but rather an asymptotic behavior indicating that the curve does not intersect the y-axis.
Conclusion
In summary, the curve -7x3y 15 does not have any real x-intercepts (it does not cross the x-axis) and does not intersect the y-axis. The mathematical representation indicates that the equation does not allow for real solutions when x or y are set to zero.
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