The function y equals negative 6 x is graphed on a coordinate plane.

Question

Question
Which statements about the graph of the function are true? Select ,begin emphasis,all,end emphasis, the true statements.

Answer options with 6 options
A.
The graph forms a curve.

B.
The graph forms a straight line.

C.
When x is greater than 0, the graph is entirely in the first quadrant.

D.
When x is less than 0, the graph is entirely in the third quadrant.

E.
When x is greater than 0, the graph is entirely in the fourth quadrant.

F.
When x is less than 0, the graph is entirely in the second quadrant.

Answer 1

Let's analyze the function \( y = -6x \).

1. Graph Behavior: The function is a linear function because it is in the form \( y = mx + b \), where \( m = -6 \) and \( b = 0 \). Thus, the graph forms a straight line.

   True Statement:

   • B. The graph forms a straight line.

2. Quadrant Analysis:

   • When \( x > 0 \): \[ y = -6x < 0 \quad \Rightarrow \quad \text{Graph is below the x-axis, which means it's in the fourth quadrant.} \]
   • When \( x < 0 \): \[ y = -6x > 0 \quad \Rightarrow \quad \text{Graph is above the x-axis, which means it's in the second quadrant.} \]

   True Statements:

   • E. When x is greater than 0, the graph is entirely in the fourth quadrant.
   • F. When x is less than 0, the graph is entirely in the second quadrant.

3. Regarding Quadrants:

   • C. is false because when \( x > 0 \), the graph does not lie in the first quadrant.
   • D. is false because when \( x < 0 \), the graph is not in the third quadrant; it is actually in the second quadrant.

Summary of the true statements:

• B. The graph forms a straight line.
• E. When x is greater than 0, the graph is entirely in the fourth quadrant.
• F. When x is less than 0, the graph is entirely in the second quadrant.