Answer: \(\frac{16}{15}\)
Explanation:
To find the sum of the x and y intercepts of the equation \(3x - 5y = 8\), you first need to find each intercept separately.
1. **X-Intercept:** To find the x-intercept, set \(y = 0\) and solve for \(x\).
\(3x - 5(0) = 8\)
\(3x = 8\)
\(x = \frac{8}{3}\)
So, the x-intercept is \(\left(\frac{8}{3}, 0\right)\).
2. **Y-Intercept:** To find the y-intercept, set \(x = 0\) and solve for \(y\).
\(3(0) - 5y = 8\)
\(-5y = 8\)
\(y = -\frac{8}{5}\)
So, the y-intercept is \(\left(0, -\frac{8}{5}\right)\).
Now, sum the x and y intercepts:
\(\frac{8}{3} - \frac{8}{5} = \frac{40}{15} - \frac{24}{15} = \frac{16}{15}\)
So, the sum of the x and y intercepts is \(\frac{16}{15}\).