Math Problem Statement

5x+10=10y

Solution

The equation 5x+10=10y5x + 10 = 10y is a linear equation in two variables, xx and yy. Let's solve for yy in terms of xx.

Steps:

  1. Subtract 10 from both sides to isolate the term with yy on the right side: 5x=10y105x = 10y - 10

  2. Rearrange the equation by adding 10 to both sides: 5x=10y5x = 10y

  3. Divide both sides by 10 to solve for yy: y=5x10=x2y = \frac{5x}{10} = \frac{x}{2}

Thus, the equation in terms of yy is: y=x2y = \frac{x}{2}

This equation represents a line with slope 12\frac{1}{2} and a y-intercept of 0.

Do you have any questions or need further details?

Here are 5 related questions you could explore:

  1. What is the slope and intercept form of a line?
  2. How do you find the slope between two points on a line?
  3. How would you graph the equation y=x2y = \frac{x}{2}?
  4. Can we rewrite the equation in terms of xx?
  5. What is the relationship between xx and yy for different values of xx?

Tip: When solving for one variable in terms of another, always aim to isolate the variable by reversing operations step by step.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Algebra
Slope-Intercept Form

Formulas

y = mx + b
Linear equation formula ax + by = c

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 8-10