Question
Find the \( x \)-intercept and the \( y \)-intercept without graphing. \[ 2 y-8=3 x \] \( x \)-intercept \( \quad(x, y)=(\square) \) \( y \)-intercept \( \quad(x, y)=(\square) \)
Ask by Bond Gibbs. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x \)-intercept \( \left(-\frac{8}{3},\, 0\right) \)
\( y \)-intercept \( (0,\, 4) \)
Solution
**Step 1. Find the \( x \)-intercept.**
The \( x \)-intercept occurs when \( y = 0 \). Substitute \( y = 0 \) into the equation:
\[
2(0) - 8 = 3x \quad \Rightarrow \quad -8 = 3x
\]
Solve for \( x \):
\[
x = -\frac{8}{3}
\]
Thus, the \( x \)-intercept is \( \left(-\frac{8}{3},\ 0\right) \).
**Step 2. Find the \( y \)-intercept.**
The \( y \)-intercept occurs when \( x = 0 \). Substitute \( x = 0 \) into the equation:
\[
2y - 8 = 3(0) \quad \Rightarrow \quad 2y - 8 = 0
\]
Solve for \( y \):
\[
2y = 8 \quad \Rightarrow \quad y = 4
\]
Thus, the \( y \)-intercept is \( (0,\, 4) \).
**Final Answer**
\( x \)-intercept \( (x, y) = \left(-\frac{8}{3},\, 0\right) \)
\( y \)-intercept \( (x, y) = (0,\, 4) \)
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To find the \( x \)-intercept, set \( y = 0 \) in the equation \( 2y - 8 = 3x \): \[ 2(0) - 8 = 3x \implies -8 = 3x \implies x = -\frac{8}{3}. \] Thus, the \( x \)-intercept is \( (x, y) = \left(-\frac{8}{3}, 0\right) \). To find the \( y \)-intercept, set \( x = 0 \): \[ 2y - 8 = 3(0) \implies 2y - 8 = 0 \implies 2y = 8 \implies y = 4. \] Thus, the \( y \)-intercept is \( (x, y) = (0, 4) \). \( x \)-intercept \( \quad(x, y) = \left(-\frac{8}{3}, 0\right) \) \( y \)-intercept \( \quad(x, y) = (0, 4) \)
