Math Problem Statement
solve
Solution
The question asks to determine which relationship represents a function with the same rate of change as the graphed function.
Step 1: Identify the slope (rate of change) from the graph.
The graph shows a straight line, indicating a linear function. To find the rate of change (slope), use the slope formula:
From the graph, we can observe two points:
- (0, 0) and (4, 3)
Now calculate the slope:
So, the rate of change (slope) for the graphed function is .
Step 2: Examine each answer choice.
-
A:
The slope here is , since it's in the form , where . Not the correct choice because the slope is different. -
B: Table with points (0, -5), (4, -12), (8, -19), (12, -26)
Find the rate of change between points: This slope is .
Not the correct choice because the slope is negative. -
C:
The slope here is , since it's in the form , where . Not the correct choice because the slope is different. -
D: Table with points (4, -6), (8, -11), (12, -16), (16, -21)
Find the rate of change between points: This slope is , but upon checking all intervals, it's consistently the same.
Not the correct choice because the slope is negative.
Conclusion:
None of the choices given directly match the slope from the graph. There might be a mismatch between the slope of the function in the graph and the available options.
Would you like to go over more details or have further questions? Here are 5 relative questions that could expand the discussion:
- How can we derive the equation of a line given two points?
- What other ways can we calculate the rate of change from a graph?
- What is the significance of the slope in real-world applications?
- Can we determine the slope from just a table of values without graphing?
- How does a positive slope differ from a negative slope in interpreting functions?
Tip: Always look for two clear points on a graph to accurately determine the slope.
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Slope-Intercept Form
Rate of Change
Formulas
Slope = (y2 - y1) / (x2 - x1)
Theorems
Slope of a line
Suitable Grade Level
Grades 7-9