Determine whether the graph of the equation is symmetric with respect to the x-axis, y-axis, line y=x, line y=-x, or none of these.
x+y=6
Do I have to move the y and 6 to the other side of the equations or does it not matter? Also, if I do, when I test using the equation
a^2 + # = b^2
Would it be -y^2 or just y^2?
note: to check if the given equation is symmetric to x-axis or y-axis or origin (that is, y=x),,
*symmetric to x-axis: change y to -y and substitute to the given equation. if it goes back to original form, therefore, it is symmetric to x-axis. otherwise, it is not.
*symmetric to y-axis: change x to -x and substitute to the given equation. if it goes back to original form, therefore, it is symmetric to y-axis. otherwise, it is not.
*symmetric to origin: change x to -x and y to -y and substitute them to the given equation. if it goes back to original form, therefore, it is symmetric to origin. otherwise, it is not.
the given equation is x+y=6,, let's check for symmetry:
*x-axis (y becomes -y)
x-y=6 ==> NOT symmetric to x-axis [since it did not go back to original form, which is x+y=6]
*y-axis (x becomes -x)
-x+y=6 ==> NOT symmetric to y-axis
*origin (x and y becomes negative)
-x-y=6 ==> NOT symmetric to origin (or y=x)
you can also check symmetry by graphing the equation,,
so there, =)
This is certainly not calculus, no does either statement make sense. I suspect something is missing.
Please put the proper subject in the heading.
To determine whether the graph of the equation x+y=6 is symmetric with respect to the x-axis, y-axis, line y=x, line y=-x, or none of these, we can follow these steps:
Step 1: Rearrange the equation into slope-intercept form (y = mx + b) if possible.
For the equation x+y=6:
- We can rewrite it as y = -x + 6 by moving the x to the right-hand side.
Step 2: Analyze the coefficients in the rearranged equation.
In y = -x + 6:
- The coefficient of x is -1.
- The coefficient of y is 1.
- The constant term is 6.
Step 3: Determine the symmetry based on the coefficients.
- If the coefficient of x and the coefficient of y are equal in magnitude (but with opposite signs), then the graph is symmetric with respect to the line y=x.
- If the coefficient of x is -1 (or any negative number) and the coefficient of y is 1 (or any positive number), then the graph is symmetric with respect to the line y=-x.
- If the coefficient of x is 0 (or any number) and the coefficient of y is 1 (or any positive number), then the graph is symmetric with respect to the y-axis.
- If the coefficient of x is -1 (or any negative number) and the coefficient of y is 0 (or any number), then the graph is symmetric with respect to the x-axis.
In our rearranged equation y = -x + 6, the coefficients of x and y are different in magnitude (but with opposite signs). Therefore, the graph is not symmetric with respect to the x-axis, y-axis, or line y=x.
Step 4: The equation does not involve any quadratic expressions like a^2 + # = b^2, so there is no need to convert any terms to the form of y^2.
In summary, the graph of the equation x+y=6 is not symmetric with respect to the x-axis, y-axis, line y=x, or line y=-x.
To determine whether the graph of the equation is symmetric with respect to the x-axis, y-axis, line y=x, line y=-x, or none of these, you can follow these steps:
1. Start with the given equation: x + y = 6.
2. To test symmetry with respect to the x-axis, replace y with -y in the equation. If the resulting equation remains the same, then the graph is symmetric with respect to the x-axis. In this case, replacing y with -y, we get x - y = 6.
3. To test symmetry with respect to the y-axis, replace x with -x in the equation. If the resulting equation stays the same, then the graph is symmetric with respect to the y-axis. In this case, replacing x with -x, we get -x + y = 6.
4. To test symmetry with respect to the line y = x, interchange x and y in the equation. If the resulting equation remains unchanged, then the graph is symmetric with respect to the line y = x. In this case, interchanging x and y, we get y + x = 6.
5. To test symmetry with respect to the line y = -x, interchange x and y in the equation and change the sign of y. If the resulting equation remains the same, then the graph is symmetric with respect to the line y = -x. In this case, interchanging x and y and changing the sign of y, we get -y + x = 6.
Now, let's solve the equation a^2 + # = b^2. The # represents a term that you want to solve for.
- If you want to solve for a term subtracted from b^2, it would be -y^2.
- If you want to solve for a term added to b^2, it would be +y^2.
I hope this helps! Let me know if you have any further questions.