Question 389269
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Hi, 
Note: the standard slope-intercept form for an equation of a line y = mx + b 
 where m is the slope and b the y-intercept.         
line that is perpendicular to –4x – 8y = 24  OR y = (-1/2)x - 3    m = -1/2
Perpendicular lines have slopes that are negative reciprocals of one another
NEW line has slope m = 2
 y = 2x + b   Using ordered pair (4,-1) to solve for b
 -1 = 8 + b    b = -9
 y = 2x - 9
{{{drawing(300,300, -10,10,-10,10,
 grid(1),
circle(0, -3,0.4),
circle(0, -9,0.4),
circle(4, -1,0.4),

graph( 300, 300, -10,10,-10,10,-.5x-3,2x-9))}}}