Question
Put the following equation of a line into slope-intercept form, simplifying all fractions. \[ 3 x+18 y=-144 \]
Ask by Lee Love. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation in slope-intercept form is \( y = -\frac{1}{6}x - 8 \).
Solution
To convert the equation \( 3x + 18y = -144 \) into slope-intercept form (\( y = mx + b \)), follow these steps:
1. **Isolate the \( y \)-term:**
\[
18y = -3x - 144
\]
2. **Divide every term by 18 to solve for \( y \):**
\[
y = \frac{-3x}{18} + \frac{-144}{18}
\]
3. **Simplify the fractions:**
\[
y = -\frac{1}{6}x - 8
\]
So, the equation in slope-intercept form is:
\[
y = -\frac{1}{6}x - 8
\]
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Simplify this solution Beyond the Answer
To put the equation \( 3x + 18y = -144 \) into slope-intercept form, we need to solve for \( y \). First, isolate the \( y \) term: \[ 18y = -144 - 3x \] Next, simplify the right side: \[ 18y = -3x - 144 \] Now, divide the entire equation by \( 18 \) to solve for \( y \): \[ y = -\frac{3}{18}x - \frac{144}{18} \] Simplifying the fractions gives: \[ y = -\frac{1}{6}x - 8 \] So, the slope-intercept form of the equation is: \[ y = -\frac{1}{6}x - 8 \]
