46. The line $y=\frac{5}{4} x-\frac{95}{4}$ intersects the $x$-axis and $y$-axis at points $A, B$, respectively. The number of points on segment $AB$ (including endpoints $A, B$) with both integer coordinates is $\qquad$.

Translating the text to English while preserving the original format and line breaks:

46. The line $y=\frac{5}{4} x-\frac{95}{4}$ intersects the $x$-axis and $y$-axis at points $A, B$, respectively. The number of points on segment $AB$ (including endpoints $A, B$) with both integer coordinates is $\qquad$.

To solve this problem, we need to find the points where the line intersects the $x$-axis and $y$-axis, and then determine the integer coordinate points on the line segment between these two points.

1. **Find the $x$-intercept (point $A$):**
   - Set $y = 0$ in the equation $y = \frac{5}{4} x - \frac{95}{4}$.
   - $0 = \frac{5}{4} x - \frac{95}{4}$
   - $\frac{5}{4} x = \frac{95}{4}$
   - $5x = 95$
   - $x = 19$
   - So, the $x$-intercept is $A(19, 0)$.

2. **Find the $y$-intercept (point $B$):**
   - Set $x = 0$ in the equation $y = \frac{5}{4} x - \frac{95}{4}$.
   - $y = -\frac{95}{4}$
   - So, the $y$-intercept is $B(0, -\frac{95}{4})$.

3. **Determine the integer coordinate points on the line segment $AB$:**
   - The line equation is $y = \frac{5}{4} x - \frac{95}{4}$.
   - For both $x$ and $y$ to be integers, $\frac{5}{4} x - \frac{95}{4}$ must be an integer.
   - This implies that $\frac{5x - 95}{4}$ must be an integer.
   - Therefore, $5x - 95$ must be divisible by 4.
   - $5x - 95 \equiv 0 \pmod{4}$
   - $5x \equiv 95 \pmod{4}$
   - Since $5 \equiv 1 \pmod{4}$, we have $x \equiv 95 \pmod{4}$
   - $95 \div 4 = 23$ remainder $3$, so $95 \equiv 3 \pmod{4}$
   - Thus, $x \equiv 3 \pmod{4}$
   - The possible values of $x$ are $3, 7, 11, 15, 19$ (since $x$ must be between 0 and 19).

4. **Check the corresponding $y$ values:**
   - For $x = 3$: $y = \frac{5}{4} \cdot 3 - \frac{95}{4} = \frac{15 - 95}{4} = -20$
   - For $x = 7$: $y = \frac{5}{4} \cdot 7 - \frac{95}{4} = \frac{35 - 95}{4} = -15$
   - For $x = 11$: $y = \frac{5}{4} \cdot 11 - \frac{95}{4} = \frac{55 - 95}{4} = -10$
   - For $x = 15$: $y = \frac{5}{4} \cdot 15 - \frac{95}{4} = \frac{75 - 95}{4} = -5$
   - For $x = 19$: $y = \frac{5}{4} \cdot 19 - \frac{95}{4} = \frac{95 - 95}{4} = 0$

So, the integer coordinate points on the line segment $AB$ are $(3, -20)$, $(7, -15)$, $(11, -10)$, $(15, -5)$, and $(19, 0)$.

Therefore, the number of points on segment $AB$ with both integer coordinates is $\boxed{5}$.
answer: 5