Find the x- and y-intercepts of the graph of 4, x, plus, 6, y, equals, 164x+6y=16. State each answer as an integer or an improper fraction in simplest form.
as usual, the user's misuse of text copying messed things up. He wrote
4, x, plus, 6, y, equals, 164x+6y=16
but duplicated the math part. That means the real equation was
4x+6y=16
so, dividing by 16, we have
x/4 + y/(8/3) = 1
giving us the intercepts of (4,0) and (0,8/3)
You are correct, my apologies for the confusion. The correct equation is $4x+6y=16$.
To find the x-intercept, we substitute $y=0$ into the equation and solve for $x$. We have $4x+6(0)=16$, so $4x=16$ and $x=4$. Therefore, the x-intercept is $(4, 0)$.
To find the y-intercept, we substitute $x=0$ into the equation and solve for $y$. We have $4(0)+6y=16$, so $6y=16$ and $y=\frac{16}{6}=\frac{8}{3}$. Therefore, the y-intercept is $\left(0, \frac{8}{3}\right)$.
To find the x-intercept, we substitute $y=0$ into the equation $164x+6y=16$ and solve for $x$. We have $164x+6(0)=16$, so $164x=16$ and $x=\frac{16}{164}=\frac{2}{41}$.
To find the y-intercept, we substitute $x=0$ into the equation $164x+6y=16$ and solve for $y$. We have $164(0)+6y=16$, so $6y=16$ and $y=\frac{16}{6}=\boxed{\frac83}$.