Answer: B
Step-by-step explanation:
The equation [tex]y+2=\frac{3}{4} x-8[/tex] is not yet in slope-intercept form([tex]y=mx+b[/tex]). Simply subtract 2 from both sides to turn the equation into slope intercept form as [tex]y=\frac{3}{4}x-10[/tex]. For a line to be perpendicular to another, it must have an opposite reciprocal slope. A reciprocal is the fraction reversed, where the numerator is the denominator and vice versa. Thus, 3/4 would become 4/3. The opposite reciprocal of 3/4 would be -4/3.
The slope of the line given is 3/4. Thus, simply plug in the opposite reciprocal of 3/4 for the slope to get: [tex]y=-\frac{4}{3} x+b[/tex]. Then, because the line passes through -12, 1, plug those values in for x and y, respectively.
[tex]1=-\frac{4}{3}*-12+b[/tex]
[tex]1=16+b[/tex]
[tex]-15=b[/tex]
Thus, the equation of the line is [tex]y=-\frac{4}{3} x-15[/tex], or B.
Hope it helps :D
