We are tasked with converting the equation \( y = -\frac{1}{80}x + \frac{1280}{40} \) into the form \( ax + by + d = 0 \).

### Step 1: Simplify the constants
Simplify the constant terms on the right-hand side:

\[
y = -\frac{1}{80}x + \frac{1280}{40}
\]

First, simplify \( \frac{1280}{40} \):

\[
\frac{1280}{40} = 32
\]

So the equation becomes:

\[
y = -\frac{1}{80}x + 32
\]

### Step 2: Rearrange into the form \( ax + by + d = 0 \)
To rewrite the equation in the form \( ax + by + d = 0 \), follow these steps:

1. Multiply both sides by 80 to eliminate the fraction:
   
   \[
   80y = -x + 80 \times 32
   \]

2. Simplify:

   \[
   80y = -x + 2560
   \]

3. Rearrange the terms to bring everything to one side of the equation:

   \[
   x + 80y - 2560 = 0
   \]

### Final Answer:
The equation in the form \( ax + by + d = 0 \) is:

\[
x + 80y - 2560 = 0
\]

Would you like any further details or explanations? Here are 5 related questions to practice similar problems:

1. How would you convert \( y = 3x - 5 \) to \( ax + by + d = 0 \)?
2. How can we rearrange \( y = \frac{2}{5}x + 7 \) into standard form?
3. If given \( y = mx + b \), what are the general steps to convert it to standard form?
4. What does the standard form of a linear equation tell us about the line it represents?
5. How would you convert a linear equation in standard form back to slope-intercept form?

**Tip:** Always try to clear fractions by multiplying both sides of the equation by the denominator when converting to standard form.

Learn how to convert the linear equation y = -1/80x + 1280/40 into the standard form ax + by + d = 0. This step-by-step solution simplifies constants and rearranges terms to express the equation in a more general form. Suitable for Grades 9-11.

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