Pregunta
Find the \( x \) - and \( y \)-intercepts (if they exist), and graph the line. \[ 3 x+4 y=8 \] Part: \( \mathbf{0} / \mathbf{3} \) Part 1 of 3 Write the intercept as an ordered pair. Select "None" if applicable. \( x \)-intercept: \( \square \)
Ask by Edwards Turnbull. in the United States
Jan 29,2025
Solución de inteligencia artificial de Upstudy
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\( x \)-intercept: \( \left( \frac{8}{3},\ 0 \right) \)
Solución
To find the \( x \)-intercept of the equation \( 3x + 4y = 8 \), follow these steps:
1. **Set \( y = 0 \):**
\[
3x + 4(0) = 8 \implies 3x = 8
\]
2. **Solve for \( x \):**
\[
x = \frac{8}{3}
\]
3. **Write the \( x \)-intercept as an ordered pair:**
\[
\left( \frac{8}{3},\ 0 \right)
\]
**\( x \)-intercept:** \( \left( \frac{8}{3},\ 0 \right) \)
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Simplifique esta solución The Deep Dive
To find the \( x \)-intercept, set \( y = 0 \) in the equation \( 3x + 4y = 8 \): \[ 3x + 4(0) = 8 \] \[ 3x = 8 \] \[ x = \frac{8}{3} \] Thus, the \( x \)-intercept is \( \left(\frac{8}{3}, 0\right) \). Now, let’s find the \( y \)-intercept by setting \( x = 0 \): \[ 3(0) + 4y = 8 \] \[ 4y = 8 \] \[ y = 2 \] So, the \( y \)-intercept is \( (0, 2) \). Now we have the intercepts: \( x \)-intercept: \( \left(\frac{8}{3}, 0\right) \) \( y \)-intercept: \( (0, 2) \)
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