What are the x-intercepts of y=(x-6)(y-9)?
they are where y=0. If the product of two factors is zero, one of the factors must be zero. So, set them to zero and solve for x:
x-6 = 0
means x = 6
and similarly for the other factor.
I also need the other intercept. How would go about figuring it out?
Please and thank you, Steve.
Well, if we're looking for the x-intercepts, that means we want to find the values of x where the equation y = (x - 6)(y - 9) crosses the x-axis. To find these intercepts, we set y = 0.
So, let's substitute y = 0 into the equation:
0 = (x - 6)(0 - 9)
Now, we have 0 = (x - 6)(-9).
Hmmm... multiplying anything by 0 makes it zero, so no matter what value x is, the equation equals zero when y is zero.
In other words, the x-intercept is the entire x-axis! So, there are infinitely many x-intercepts for this equation! Isn't that a bit greedy?
To find the x-intercepts of the equation, we need to set y equal to zero and solve for x.
Given the equation: y = (x - 6)(y - 9)
Setting y = 0, we have: 0 = (x - 6)(0 - 9)
Simplifying, we get: 0 = (x - 6)(-9)
To solve for x, we set each factor equal to zero:
x - 6 = 0 or -9 = 0
The second equation, -9 = 0, has no solution since 9 is not equal to 0.
Solving the first equation, we get:
x = 6
So, the x-intercept is x = 6.
To find the x-intercepts of a given equation, we need to set y equal to zero and solve for the corresponding values of x. In this case, we have the equation y = (x-6)(y-9).
Step 1: Set y = 0. Since the equation is y = (x-6)(y-9), substitute y with 0.
0 = (x-6)(0-9).
Step 2: Simplify the equation.
0 = (x-6)(-9).
0 = -9(x-6).
Step 3: Set each factor equal to zero and solve for x.
Setting x-6 = 0, we can add 6 to both sides of the equation.
x = 6.
Therefore, the x-intercept is 6.
To summarize, the x-intercept of the given equation y = (x-6)(y-9) is x = 6.