Question
Find both the \( x \)-intercept and the \( y \)-intercept of \[ 7.8 x-6.8 y+5.6=0 \] Round your answers to two decimal places.
Ask by Ray Dunn. in the United States
Jan 08,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The \( x \)-intercept is approximately \( -0.72 \) and the \( y \)-intercept is approximately \( 0.82 \).
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Beyond the Answer
To find the \( x \)-intercept, set \( y = 0 \) in the equation: \[ 7.8x - 6.8(0) + 5.6 = 0 \] \[ 7.8x + 5.6 = 0 \] \[ 7.8x = -5.6 \] \[ x = \frac{-5.6}{7.8} \approx -0.72 \] So, the \( x \)-intercept is approximately \( (-0.72, 0) \). Now, to find the \( y \)-intercept, set \( x = 0 \): \[ 7.8(0) - 6.8y + 5.6 = 0 \] \[ -6.8y + 5.6 = 0 \] \[ -6.8y = -5.6 \] \[ y = \frac{5.6}{6.8} \approx 0.82 \] Thus, the \( y \)-intercept is approximately \( (0, 0.82) \). In summary, the \( x \)-intercept is \( (-0.72, 0) \) and the \( y \)-intercept is \( (0, 0.82) \).
