Question
13) Write each equation in slope-interce \( -2 y=3 x-4 \)
Ask by Murray Chen. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation \(-2y = 3x - 4\) in slope-intercept form is \(y = -\frac{3}{2}x + 2\).
Solution
To rewrite the equation \(-2y = 3x - 4\) in **slope-intercept form** (\(y = mx + b\)), follow these steps:
1. **Isolate \(y\):**
\[
-2y = 3x - 4
\]
2. **Divide both sides by \(-2\) to solve for \(y\):**
\[
y = \frac{3x - 4}{-2}
\]
Simplify the fractions:
\[
y = -\frac{3}{2}x + 2
\]
**Final Slope-Intercept Form:**
\[
y = -\frac{3}{2}x + 2
\]
- **Slope (\(m\))**: \(-\frac{3}{2}\)
- **Y-intercept (\(b\))**: \(2\)
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Simplify this solution Beyond the Answer
To convert the equation \(-2y = 3x - 4\) into slope-intercept form, which is \(y = mx + b\), start by dividing every term by -2. This gives you \(y = -\frac{3}{2}x + 2\). Here, the slope \(m\) is \(-\frac{3}{2}\) and the y-intercept \(b\) is \(2\), meaning the line crosses the y-axis at the point (0, 2). Understanding slope-intercept form is super handy in real life! For instance, if you're graphing sales over time, the slope can represent the rate of sales increase or decrease, while the y-intercept shows your initial sales at the start of the period. It's a great way to visualize trends and make predictions!
