To describe the graph of the proportional relationship represented by the equation [tex]\( y = 3.5x \)[/tex], let's analyze the equation step by step.
1. Identify the type of equation:
The given equation [tex]\( y = 3.5x \)[/tex] is a linear equation in the form [tex]\( y = mx \)[/tex], where [tex]\( m \)[/tex] is the slope. In this case, the slope [tex]\( m \)[/tex] is 3.5.
2. Determine key points on the graph:
To graph this equation, we can use specific values of [tex]\( x \)[/tex] to find corresponding values of [tex]\( y \)[/tex].
- When [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 3.5 \cdot 0 = 0
\][/tex]
This gives us the point [tex]\( (0, 0) \)[/tex].
- When [tex]\( x = 1 \)[/tex]:
[tex]\[
y = 3.5 \cdot 1 = 3.5
\][/tex]
This gives us the point [tex]\( (1, 3.5) \)[/tex].
3. Plot these points and determine the line:
The points [tex]\( (0, 0) \)[/tex] and [tex]\( (1, 3.5) \)[/tex] can be plotted on a coordinate plane. A straight line connecting these two points represents the graph of the equation.
4. Conclusion:
Based on the points calculated, the graph is a line through the points [tex]\( (0, 0) \)[/tex] and [tex]\( (1, 3.5) \)[/tex].
Therefore, the correct description of the graph of this proportional relationship is:
- The graph is a line that goes through points [tex]\( (0, 0) \)[/tex] and [tex]\( (1, 3.5) \)[/tex].
