Possible number of lines

Let the x-intercept of the line be $(x_1, 0)$ , and the y-intercept be $(0, y_1)$ . Then the slope of the line is $-\frac{y_1}{x_1}$ and the equation $y - y_1 = -\frac{y_1}{x_1} x$ . We can substitute the point (4, 3) into this equation to get $3 = -\frac{4y_1}{x_1} + y_1$ . The rest is nonrigorous casework. Starting from observation when $x_1 = 2, 3, 5$ , etc. we see that the sets $(x_1, y_1)$ that allow for such line include (5, 15) and (7, 7).

only x intercept y=3 and the y intercept x=4. will pass through the point (4,3)