Question
Rewrite the polynomial in the form \( a x+b y+c \) and then identify the values of \( a, b \), and \( c \). \[ \frac{y}{5}-1-8 x \]
Ask by Savage Parry. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The polynomial \(\frac{y}{5} - 1 - 8x\) can be rewritten as \(-8x + \frac{1}{5}y - 1\). The coefficients are:
- \(a = -8\)
- \(b = \frac{1}{5}\)
- \(c = -1\)
Solution
To rewrite the polynomial \(\frac{y}{5} - 1 - 8x\) in the form \(a x + b y + c\), follow these steps:
1. **Arrange the Terms:**
\[
\frac{y}{5} - 8x - 1
\]
2. **Express with Coefficients:**
\[
-8x + \frac{1}{5}y - 1
\]
So, the polynomial in the desired form is:
\[
-8x + \frac{1}{5}y - 1
\]
**Identified Coefficients:**
- \(a = -8\)
- \(b = \frac{1}{5}\)
- \(c = -1\)
**Summary:**
\[
\boxed{-8x + \frac{1}{5}y - 1 \quad \text{where} \quad a = -8,\ b = \frac{1}{5},\ \text{and}\ c = -1}
\]
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Simplify this solution The Deep Dive
To rewrite the polynomial \( \frac{y}{5}-1-8 x \) in the form \( ax + by + c \), we first rearrange the terms. We can express \( \frac{y}{5} \) as \( \frac{1}{5}y \): \[ -8x + \frac{1}{5}y - 1 \] Now it’s clearer that: - \( a = -8 \) - \( b = \frac{1}{5} \) - \( c = -1 \) Thus, the polynomial in the form \( ax + by + c \) is \( -8x + \frac{1}{5}y - 1 \), with \( a = -8 \), \( b = \frac{1}{5} \), and \( c = -1 \).
