Answer
$x+7y=-4$
Work Step by Step
We know that if the slope of two lines are opposite reciprocals, they are perpendicular. Thus, we find the opposite reciprocal of the given line and plug in the given point into the point-slope equation for a line, which is: $$y_2-y_1=m(x_2-x_1)$$ We first find m: $$\frac{y_2-y_1}{x_2-x_1}$$ $$m= \frac{0+1}{-4-3}= -1/7$$ We know use the point slope form given above: $$y_2-y_1=m(x_2-x_1)$$ $$y-0==-1/7(x+4)$$ Now, we use PEMDAS, a method for simplification. This acronym reminds us that we must first address parentheses, and then exponents. Next, we address multiplication and division, going from left to right. Lastly, we simplify addition and subtraction from left to right. This gives: $x+7y=-4$