Find the intercepts and use them to graph the equation Y=x-4 A. The intercept(s) is/are (answer)
B. There are no intercepts.

x-intercepts: (1,0), (-1,0)

y-intercept: (0,2), (0,-2)

Step-by-step explanation:

We are given the following in the equation:

4x^2+y^2 = 44x

2

+y

2

=4

x-intercept:

It is the value of x for which y is zero.

$$\begin{lgathered}4x^2 + (0)^2 = 4\\4x^2 = 4\\x^2 = 1\\x = \pm 1\end{lgathered}$$

x-intercepts: (1,0), (-1,0)

y-intercept:

It is the value of y for which x i 0.

$$\begin{lgathered}4(0)^2 + y^2 = 4\\y^2 = 4\\y = \pm 2\end{lgathered}$$

y-intercept: (0,2), (0,-2)

Symmetry around y-axis:

$$\begin{lgathered}4(-x)^2 + y^2 =4 \\4x^2 + y^2 = 4\end{lgathered}$$

Thus, it is symmetric around y-axis.

Symmetry around x-axis:

$$\begin{lgathered}4x^2 + (-y)^2 = 4\\4x^2 + y^2 = 4\end{lgathered}$$

Thus, it is symmetric around x-axis.

Symmetry around origin:

$$\begin{lgathered}4(-x)^2 + (-y)^2 = 4\\4x^2 + y^2 = 4\end{lgathered}$$

Thus, it is symmetric around origin