Put the following equation of a line into slope-intercept form, simplifying all fractions. 4x+4y=32

To convert the equation \( 4x + 4y = 32 \) into slope-intercept form, which is \( y = mx + b \), follow these steps:

1. Start with the given equation:
   \[
   4x + 4y = 32
   \]

2. Subtract \( 4x \) from both sides to isolate the \( y \)-term:
   \[
   4y = -4x + 32
   \]

3. Divide every term by 4 to simplify:
   \[
   y = -x + 8
   \]

The equation in slope-intercept form is:
\[
y = -x + 8
\]

In this form, the slope \( m \) is \( -1 \), and the y-intercept \( b \) is \( 8 \).

Would you like more details or have any questions?

Here are five related questions:
1. What is the slope of the line represented by \( y = -x + 8 \)?
2. How would the graph of \( y = -x + 8 \) look like?
3. What is the x-intercept of the line \( y = -x + 8 \)?
4. How do you find the slope from two points on a line?
5. How would you rewrite the equation \( y = -x + 8 \) in standard form?

**Tip:** In the slope-intercept form \( y = mx + b \), \( m \) represents the slope of the line, and \( b \) represents the y-intercept.

Put the following equation of a line into slope-intercept form, simplifying all fractions. 4x + 4y = 32

Learn how to convert the linear equation 4x + 4y = 32 into slope-intercept form (y = mx + b). Follow a detailed step-by-step solution to simplify the equation, identify the slope and y-intercept, and understand key algebraic concepts. Suitable for students in Grades 8-10.

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