Math Problem Statement

5x+2y=10 the slope intercept of the equation is

Solution

To write the equation 5x+2y=105x + 2y = 10 in slope-intercept form (y=mx+by = mx + b, where mm is the slope and bb is the y-intercept), we need to solve for yy.

Step-by-step process:

  1. Start with the given equation: 5x+2y=105x + 2y = 10

  2. Subtract 5x5x from both sides to isolate the yy term: 2y=5x+102y = -5x + 10

  3. Divide both sides of the equation by 2 to solve for yy: y=5x+102y = \frac{-5x + 10}{2}

  4. Simplify the right-hand side: y=52x+5y = -\frac{5}{2}x + 5

Slope-Intercept Form:

The equation is now in slope-intercept form: y=52x+5y = -\frac{5}{2}x + 5

  • Slope (mm): 52-\frac{5}{2}
  • Y-intercept (bb): 55

Conclusion

The slope of the line is 52-\frac{5}{2}, and the y-intercept is 55.

Would you like more details or have any questions?

Related Questions:

  1. How would you convert 3x+4y=123x + 4y = 12 into slope-intercept form?
  2. What is the slope of the equation 2x+y=82x + y = 8?
  3. How do you find the x-intercept and y-intercept of a line from its equation?
  4. Can you explain how to graph the line y=52x+5y = -\frac{5}{2}x + 5?
  5. How do you convert the equation x=4x = 4 into slope-intercept form?

Tip:

To convert an equation into slope-intercept form, focus on isolating yy on one side. Once yy is by itself, the coefficient of xx gives you the slope, and the constant term is the y-intercept.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

Slope-Intercept Form: y = mx + b

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 8-10