Answer :
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].
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].
