Math Problem Statement

Identify the slope and y-intercept. Then, graph the linear equation: y = -2/3x + 5.

Solution

The linear equation given is:

y=23x+5y = -\frac{2}{3}x + 5

From this equation, we can identify:

  1. The y-intercept (bb): The y-intercept is the constant term, which is 55. This means that the line crosses the y-axis at y=5y = 5.

  2. The slope (mm): The slope is the coefficient of xx, which is 23-\frac{2}{3}. This means for every 3 units you move to the right (positive x-direction), the line goes down by 2 units (negative y-direction).

To graph this equation:

  1. Start at the y-intercept, (0,5)(0, 5).
  2. Use the slope, 23-\frac{2}{3}, to find the next point by moving 3 units to the right and 2 units down.

Would you like further details on any of these steps?

Here are some related questions you might find helpful:

  1. How can I interpret the slope in practical terms?
  2. What does a negative slope imply about the direction of the line?
  3. How would the graph change if the y-intercept was negative?
  4. What if the slope was positive instead of negative?
  5. How can I find the x-intercept from this equation?

Tip: When working with slopes, remember that a negative slope means the line falls as it moves from left to right, while a positive slope means it rises.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

Slope-intercept form y = mx + b

Theorems

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Suitable Grade Level

Grade 8-10