Let's first convert the equation of the line given to slope-intercept form:
[tex]y=\frac{1}{4}x +\frac{1}{2}[/tex]
We know that the slope (m in y = mx + b) is 1/4. A perpendicular line always has a negative reciprocal slope. So, the equation of the perpendicular line in slope-intercept form is simply:
[tex]y= -4x + \frac{1}{2}[/tex]
But, since they give us two points on the line, we'll put that equation in point-slope form (y - k = m(x - h)):
[tex]y - 3 = -4(x+3)[/tex]
So, your final answer is y - 3 = -4(x + 3).
