Let's delve into the problem step-by-step:
1. Understanding the Original Equation:
The original equation given is:
[tex]\[
c = -1.75 + 1.75m
\][/tex]
In this equation:
- [tex]\( c \)[/tex] represents the total charge in dollars.
- [tex]\( m \)[/tex] represents the number of miles traveled.
- The term [tex]\(-1.75\)[/tex] is the y-intercept, which indicates where the graph crosses the y-axis when [tex]\( m = 0 \)[/tex].
- The term [tex]\(1.75m\)[/tex] represents the slope of the graph.
2. Understanding the Slope:
- The slope of [tex]\( 1.75m \)[/tex] means that for every additional mile traveled, the charge increases by [tex]$1.75.
3. Modification of the Equation:
The question states that the coefficient of \( m \) changes from 1.75 to 1.25. Therefore, the new equation will be:
\[
c = -1.75 + 1.25m
\]
Here, the slope has changed to 1.25.
4. Comparing the Slopes:
- Original slope: \( 1.75 \)
- New slope: \( 1.25 \)
Since \( 1.25 \) is less than \( 1.75 \), let's analyze the implication of this change in slope:
5. Impact on the Graph:
- Slope: A smaller slope means that for each mile traveled, the charge now increases by a smaller amount ($[/tex]1.25 instead of $1.75).
- Graph Steepness: The graph of the new equation will be less steep than the original graph. In other words, the graph becomes flatter.
- Y-Intercept: Notice that the y-intercept [tex]\(-1.75\)[/tex] remains unchanged, indicating that both graphs will start at the same point on the y-axis (when [tex]\( m = 0 \)[/tex]).
6. Conclusion:
- The y-intercept remains the same, so the graph does not start higher or lower on the y-axis.
- The graph does not become steeper; instead, it becomes flatter due to the reduced slope.
Thus, the correct observation about the change in the graph is:
The graph will be flatter.
