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 y=2x+5y = -2x + 5. I can verify whether the graph accurately represents the line by analyzing the slope and intercept provided by the equation.

Step-by-Step Analysis:

  1. Slope (mm):

    • The slope of the line is 2-2. This means the line should go down 2 units for every 1 unit increase in xx.
  2. Y-Intercept (bb):

    • The yy-intercept is 55. This indicates the point (0,5)(0, 5) is on the line.
  3. Checking the Graph:

    • The line should start at (0,5)(0, 5) and slope downward with a rise/run of 2/1-2/1.
    • To verify, let’s compute a few other points on the line:
      • When x=1x = 1: y=2(1)+5=3y = -2(1) + 5 = 3. The point (1,3)(1, 3) should be on the graph.
      • When x=1x = -1: y=2(1)+5=7y = -2(-1) + 5 = 7. The point (1,7)(-1, 7) 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 (mm) were 00.

Let me know if you want further clarification or a corrected graph!

Related Questions:

  1. What steps are needed to accurately plot a linear equation like y=2x+5y = -2x + 5?
  2. How does the slope affect the angle of the line?
  3. How do you determine whether a graph represents an equation correctly?
  4. What does it mean if a line is horizontal or vertical in a graph?
  5. 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