Question

Find the​ x-intercept and the​ y-intercept. Then graph the equation.
yequals2
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Part 1
Choose the correct​ x-intercept below.
A.left parenthesis 2 comma 0 right parenthesis
left parenthesis 2 comma 0 right parenthesis
B.
none
C.left parenthesis 0 comma 2 right parenthesis
left parenthesis 0 comma 2 right parenthesis

Answer 1

The equation given is \( y = 2 \). This represents a horizontal line where the value of \( y \) is always 2, regardless of the value of \( x \).

### Finding Intercepts:

1. **Y-intercept:**
To find the y-intercept, set \( x = 0 \):
\[
y = 2
\]
So, the y-intercept is \( (0, 2) \).

2. **X-intercept:**
To find the x-intercept, set \( y = 0 \):
\[
0 = 2
\]
This equation is not true for any value of \( x \). Therefore, there is no x-intercept.

### Summary of Intercepts:
- **X-intercept:** None
- **Y-intercept:** \( (0, 2) \)

### Choosing x-intercept option:
Given the options provided:
- A. \( (2, 0) \)
- B. None (correct choice)
- C. \( (0, 2) \)

The correct choice for the x-intercept is **B. None**.

### Graphing the Equation:
The graph of the equation \( y = 2 \) is a horizontal line that intersects the y-axis at the point \( (0, 2) \) and extends infinitely to the left and right. There are no x-intercepts.

You can visualize this by drawing a horizontal line that crosses the y-axis at the point \( (0, 2) \).