Pregunta
Rewrite the equation \( 3 x-4 y=12 \) in slope-intercept form, solving for \( y \). Show your work.
Ask by Floyd Tyler. in the United States
Jan 23,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
To rewrite \( 3x - 4y = 12 \) in slope-intercept form, solve for \( y \):
1. Subtract \( 3x \) from both sides:
\[
-4y = -3x + 12
\]
2. Divide every term by \( -4 \):
\[
y = \frac{3}{4}x - 3
\]
So, the slope-intercept form is:
\[
y = \frac{3}{4}x - 3
\]
Solución
To rewrite the equation \( 3x - 4y = 12 \) into **slope-intercept form** (\( y = mx + b \)), where \( m \) is the slope and \( b \) is the y-intercept, follow these steps:
1. **Start with the original equation:**
\[
3x - 4y = 12
\]
2. **Isolate the term containing \( y \) by moving \( 3x \) to the other side:**
\[
-4y = -3x + 12
\]
3. **Solve for \( y \) by dividing every term by \( -4 \):**
\[
y = \frac{-3x + 12}{-4}
\]
4. **Simplify the equation:**
\[
y = \frac{3}{4}x - 3
\]
So, the **slope-intercept form** of the equation is:
\[
y = \frac{3}{4}x - 3
\]
**Interpretation:**
- **Slope (\( m \))**: \( \frac{3}{4} \)
- **Y-intercept (\( b \))**: \( -3 \)
This means the line has a slope of \( \frac{3}{4} \) and crosses the y-axis at the point \( (0, -3) \).
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Simplifique esta solución Beyond the Answer
To rewrite the equation \( 3x - 4y = 12 \) in slope-intercept form, we need to solve for \( y \). 1. Start with the original equation: \( 3x - 4y = 12 \) 2. Subtract \( 3x \) from both sides: \( -4y = -3x + 12 \) 3. Now, divide every term by \(-4\) to isolate \(y\): \( y = \frac{3}{4}x - 3 \) Now, the equation is in slope-intercept form \( y = mx + b \), where the slope \( m = \frac{3}{4} \) and the y-intercept \( b = -3 \).
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