Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Describe the graph of the proportional relationship represented by the equation [tex]y = 4.5x[/tex].

A. The graph is a line that goes through points [tex](0,0)[/tex] and [tex](45,1)[/tex].
B. The graph is a line that goes through points [tex](0,0)[/tex] and [tex](45,45)[/tex].
C. The graph is a line that goes through points [tex](0,0)[/tex] and [tex](1, 4.5)[/tex].
D. The graph is a line that goes through points [tex](0,0)[/tex] and [tex](9,2)[/tex].

Sagot :

Sure, let's analyze the equation and the points where the line of this equation passes through. The equation given is \( y = 4.5x \).

Let's break this down step-by-step:

1. Points that the Graph Passes Through:

a. For \( x = 0 \):
[tex]\[ y = 4.5 \times 0 = 0 \][/tex]
This means when \( x = 0 \), \( y = 0 \). Therefore, one of the points is \((0,0)\).

b. For \( x = 1 \):
[tex]\[ y = 4.5 \times 1 = 4.5 \][/tex]
This means when \( x = 1 \), \( y = 4.5 \). Therefore, another point is \((1, 4.5)\).

2. Verifying the Relationship:
- The relationship described by \( y = 4.5x \) is a linear relationship, meaning it forms a straight line when graphed.
- The graph will pass through all points that satisfy this equation.
- The point \((0,0)\) indeed indicates that the line passes through the origin, which is characteristic of a proportional relationship.
- The point \((1,4.5)\) confirms that for every unit increase in \( x \), \( y \) increases by 4.5 units.

Given the correct points, the linear graph of the equation \( y = 4.5x \) will indeed pass through the points \((0,0)\) and \((1, 4.5)\).

The correct description from the options given would be:
- The graph is a line that goes through points [tex]\((0,0)\)[/tex] and [tex]\((1, 4.5)\)[/tex].