Answer: Any line with slope of -3/4
Reason:
Let's calculate the slope of the line through those two points
[tex](x_1,y_1) = (1,3) \text{ and } (x_2,y_2) = (4,7)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{7 - 3}{4 - 1}\\\\m = \frac{4}{3}\\\\[/tex]
The slope of the line is 4/3
Anything perpendicular to this has a slope of -3/4. I flipped the fraction and flipped the sign (from positive to negative).
So for example, the answer may be something like [tex]y = -\frac{3}{4}x+5[/tex] or [tex]y = -\frac{3}{4}x-2[/tex]. All that matters is the -3/4 out front of the x.
Side note: the original slope 4/3 and perpendicular slope -3/4 multiply to -1
