Question
Put the following equation of a line into slope-intercept form, simplifying all fractions. \[ 4 y-2 x=-8 \]
Ask by Carroll Barnett. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation in slope-intercept form is \( y = \frac{1}{2}x - 2 \).
Solution
Certainly! Let's convert the given equation into **slope-intercept form**, which is:
\[
y = mx + b
\]
where:
- \( m \) is the **slope** of the line.
- \( b \) is the **y-intercept** (the point where the line crosses the y-axis).
**Given Equation:**
\[
4y - 2x = -8
\]
**Step-by-Step Conversion:**
1. **Start with the original equation:**
\[
4y - 2x = -8
\]
2. **Isolate the \( y \)-term:**
To get \( y \) by itself on one side, add \( 2x \) to both sides of the equation:
\[
4y = 2x - 8
\]
3. **Solve for \( y \):**
Divide every term in the equation by **4** to solve for \( y \):
\[
y = \frac{2x}{4} - \frac{8}{4}
\]
4. **Simplify the fractions:**
- \( \frac{2x}{4} = \frac{1}{2}x \)
- \( \frac{8}{4} = 2 \)
So, the equation becomes:
\[
y = \frac{1}{2}x - 2
\]
**Final Slope-Intercept Form:**
\[
y = \frac{1}{2}x - 2
\]
**Interpretation:**
- **Slope (\( m \))**: \( \frac{1}{2} \)
- **y-Intercept (\( b \))**: \( -2 \)
This means the line crosses the y-axis at \( (0, -2) \) and rises \( \frac{1}{2} \) unit vertically for every 1 unit it moves horizontally.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To convert the equation \( 4y - 2x = -8 \) into slope-intercept form (\( y = mx + b \)), we need to solve for \( y \). First, isolate \( 4y \) by adding \( 2x \) to both sides: \[ 4y = 2x - 8 \] Next, divide every term by 4 to solve for \( y \): \[ y = \frac{2}{4}x - \frac{8}{4} \] Simplifying gives: \[ y = \frac{1}{2}x - 2 \] Now we have the slope-intercept form: \( y = \frac{1}{2}x - 2 \). So, the slope \( m \) is \( \frac{1}{2} \) and the y-intercept \( b \) is \( -2 \).
