Answer
point-slope form $y-5=4(x+2)$
slope-intercept form $y=4x+13$
general form $4x-y+13=0$
Work Step by Step
Step 1. Since the line is perpendicular to $y=-\frac{1}{4}+\frac{1}{3}$, which has a slope of $m_2=-\frac{1}{4}$, we see that the slope $m_1$ of the unknown line satisfies $m_1m_2=-1$, which gives $m_1=4$
Step 2. As the line passes through $(-2,5)$, we can write the point-slope form as $y-5=4(x+2)$
Step 3. Rewrite the above equation: we have $y=4x+8+5$ or $y=4x+13$, which gives the slope-intercept form.
Step 4. Rewrite the above equation as $4x-y+13=0$ to obtain the general form.
