Question

select all the statements that describe the graph of the equation x = -2. a. the graph is a horizontal line. b. the slope of the line is undefined. c. the graph passes through the ordered pair (-2, 3). d. the x-intercept of the line is (-2, 0). e. the domain is all real numbers.

Explanation:

• Option A: The equation \( x = -2 \) represents a vertical line (since all points have \( x = -2 \) and \( y \) can be any real number), not a horizontal line. So A is incorrect.
• Option B: For a vertical line, the slope is undefined (because the slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \) has a denominator of 0 when \( x_2 = x_1 \)). So B is correct.
• Option C: The ordered pair \( (-2, 3) \) has \( x = -2 \), so it lies on the line \( x = -2 \). So C is correct.
• Option D: The \( x \)-intercept is the point where \( y = 0 \) on the line. For \( x = -2 \), when \( y = 0 \), the point is \( (-2, 0) \). So D is correct.
• Option E: The domain of \( x = -2 \) is just \( x = -2 \) (only one value), not all real numbers. So E is incorrect.

Answer:

B. The slope of the line is undefined.
C. The graph passes through the ordered pair \((-2, 3)\).
D. The \( x \)-intercept of the line is \((-2, 0)\).