Pregunta
Find the \( y \)-intercept and the slope of the line. \[ \begin{array}{l}12 x+4 y=4 \\ \text { Write your answers in simplest form. } \\ y \text {-intercept: } \square\end{array} \]
Ask by Tran Norris. in the United States
Mar 16,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The slope is \(-3\) and the \( y \)-intercept is \(1\).
Solución
1. Start with the given equation:
\[
12x + 4y = 4
\]
2. Isolate the \( y \)-term by subtracting \( 12x \) from both sides:
\[
4y = 4 - 12x
\]
3. Divide each term by \( 4 \) to solve for \( y \):
\[
y = \frac{4 - 12x}{4} = 1 - 3x
\]
4. Rewrite the equation in slope-intercept form \( y = mx + b \):
\[
y = -3x + 1
\]
- The slope is:
\[
m = -3
\]
- The \( y \)-intercept is:
\[
b = 1
\]
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Simplifique esta solución Bonus Knowledge
To find the \( y \)-intercept and the slope of the line given by the equation \( 12x + 4y = 4 \), we can start by rewriting the equation in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. 1. Start with the original equation: \[ 12x + 4y = 4 \] 2. Solve for \( y \): \[ 4y = -12x + 4 \] \[ y = -3x + 1 \] From this equation, we can identify the slope \( m \) as \(-3\) and the \( y \)-intercept \( b \) as \( 1 \). So, the \( y \)-intercept is \( 1 \) and the slope is \(-3\). In simplest form: - \( y \)-intercept: \( 1 \) - Slope: \( -3 \)
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