Math Problem Statement

2x+5y=-5 Find the slope and the y-intercept. Then use them to graph the line.

Solution

We start with the given equation:

2x+5y=52x + 5y = -5

Step 1: Convert to Slope-Intercept Form (y=mx+by = mx + b)

The slope-intercept form is:

y=mx+by = mx + b

where:

  • mm is the slope
  • bb is the y-intercept

Solve for yy:

5y=2x55y = -2x - 5

y=25x1y = -\frac{2}{5}x - 1

Step 2: Identify the Slope and Y-Intercept

From the equation:

y=25x1y = -\frac{2}{5}x - 1

  • Slope (mm) = 25-\frac{2}{5}
  • Y-Intercept (bb) = 1-1 (which corresponds to the point (0,1)(0, -1))

Step 3: Graphing the Line

  1. Plot the Y-Intercept: Start by plotting the point (0,1)(0, -1).
  2. Use the Slope: The slope 25-\frac{2}{5} means:
    • Move down 2 units (negative direction).
    • Move right 5 units (positive direction).
    • Plot this second point.
  3. Draw the Line: Connect the points with a straight line extending in both directions.

Would you like a visual graph? Let me know!

Related Questions:

  1. How do you find the x-intercept of this equation?
  2. What happens to the graph if the equation changes to 2x+5y=52x + 5y = 5?
  3. How can you verify the slope using two points on the line?
  4. What does a positive slope indicate compared to a negative slope?
  5. How do you determine if two lines are parallel?

Tip:

To check if a point is on the line, substitute its xx and yy values into the equation. If both sides are equal, the point lies on the line.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

Slope-intercept form: y = mx + b
Slope formula: m = -A/B (from Ax + By = C)

Theorems

Equation of a straight line

Suitable Grade Level

Grades 7-9