SOLUTION: Write an equation of a line that is perpendicular to y = 2x + 3 and passes through (3,4).

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Question 86140This question is from textbook
: Write an equation of a line that is perpendicular to y = 2x + 3 and
passes through (3,4). This question is from textbook

Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
A LINE PERPENDICULAR TO THIS LINE [Y=2X+3] (red line)HAS A SLOPE (m) OF -1/2.
SEEING AS IT PASSES THROUGH (3,4) WE NEED TO SUBSTITUTE THESE VALUES FOR THE X & Y VALUES IN THE LINE EQUATION [Y=mX+b], ALONG WITH THE SLOPE (m=-1/2) & SOLVE FOR THE Y INTERCEPT (b).
4=-1/2*3+b
4=-3/2+b
b=4+3/2
b=4+1.5
b=5.5 THE Y INTERCEPT.
THUS WE HAVE THE LINE EQUATION:
Y=-X/2+5.5 (green line)
PROOF IN GRAPH FORM FOLLOWS:
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+y+=+2x+%2B3%2C+y+=+-x%2F2+%2B5.5%29+ (graph 300x300 pixels, x from -10 to 10, y from -10 to 10, of TWO functions y = 2x +3 and y = -x/2 +5.5).