Answer:
Step-by-step explanation:
We see that if a line is perpendicular to the line [tex]y = \frac{3}{4}x - \frac{1}{2}[/tex], then the slope of the line is [tex]-\frac{4}{3}[/tex] since the slopes of two perpendicular lines must multiply to -1. Knowing this, we get the following equation: [tex]y = -\frac{4}{3}x + b[/tex], and we can find out b by plugging in the x and y that we know. In this case, [tex]-4 = -\frac{4}{3} \cdot -6 + b[/tex], so we get [tex]b = -12[/tex]. Plugging it back into the equation, we get the final equation of [tex]\boxed{y = -\frac{4}{3}x - 12}[/tex]
