Math Problem Statement
Graph y = -2x + 5. Verify whether the graph matches the equation and identify any discrepancies.
Solution
The equation of the line in the graph is . I can verify whether the graph accurately represents the line by analyzing the slope and intercept provided by the equation.
Step-by-Step Analysis:
-
Slope ():
- The slope of the line is . This means the line should go down 2 units for every 1 unit increase in .
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Y-Intercept ():
- The -intercept is . This indicates the point is on the line.
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Checking the Graph:
- The line should start at and slope downward with a rise/run of .
- To verify, let’s compute a few other points on the line:
- When : . The point should be on the graph.
- When : . The point should also be on the graph.
The graph in the image does not appear to represent this equation accurately. Instead, it seems to show a horizontal line, which would only occur if the slope () were .
Let me know if you want further clarification or a corrected graph!
Related Questions:
- What steps are needed to accurately plot a linear equation like ?
- How does the slope affect the angle of the line?
- How do you determine whether a graph represents an equation correctly?
- What does it mean if a line is horizontal or vertical in a graph?
- Can the slope and intercept values be interpreted in real-life situations?
Tip:
When graphing a linear equation, always calculate a few points using the equation to confirm the accuracy of the plotted line!
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Graphing Linear Equations
Formulas
y = mx + b
Theorems
Slope-Intercept Form
Suitable Grade Level
Grades 8-10