Math Problem Statement

−4x+4y=12 in slope form

Solution

To convert the equation 4x+4y=12-4x + 4y = 12 into slope-intercept form, we need to solve for yy in terms of xx.

Steps:

  1. Start with the given equation: 4x+4y=12-4x + 4y = 12

  2. Add 4x4x to both sides to isolate terms with yy: 4y=4x+124y = 4x + 12

  3. Divide each term by 44 to solve for yy: y=x+3y = x + 3

Result:

The slope-intercept form is: y=x+3y = x + 3 where the slope m=1m = 1 and the y-intercept b=3b = 3.

Would you like further details or have any questions?

Further Questions:

  1. How can I graph this line using the slope and y-intercept?
  2. What would happen to the slope if the equation was 4x+8y=12-4x + 8y = 12?
  3. How can I determine if two lines are parallel given their equations?
  4. How do you convert from slope-intercept form back to standard form?
  5. What are the effects of changing the y-intercept in a linear equation?

Tip:

In the slope-intercept form, the coefficient of xx represents the slope, showing how steep the line is.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

Slope-Intercept Form y = mx + b

Theorems

Properties of Linear Equations

Suitable Grade Level

Grades 7-9