Answer:
See explanations below
Step-by-step explanation:
We are going to be using the point slope form of equation of a line for all the question, This is expressed as;
y-y0 = m(x-x0)
1) For a straight line is perpendicular to y=2x+5 and passes through (0,3).
Slope of the line m = 2
Slope of the line perpendicular M = -1/m
M = -1/2
Substituting M = -1/2 and the point (0,3) into the equation
y-y0 = m(x-x0)
y - 3 = -1/2(x-0)
y-3 = -x/2
2(y-3) = -x
2y-6 = -x
-x-2y = -6
x+2y = 6
The required equation is x+2y = 6
2) For a straight line is perpendicular to y=0.5x+3 and passes through (3,5).
Slope of the line m = 0.5
Slope of the line perpendicular M = -1/m
M = -1/0.5
M = -2
Substituting M = -2 and the point (3,5) into the equation
y-y0 = m(x-x0)
y - 5 = -2(x-3)
y-5 = -2x+6
y+2x = 6 + 5
y+2x = 11
The required equation is y+2x = 11
3) A straight line is perpendicular to y=4-5x and passes through (20,5).
Slope of the line m = -5
Slope of the line perpendicular M = -1/m
M = -1/-5
M = 1/5
Substituting M = -2 and the point (20,5) into the equation
y-y0 = m(x-x0)
y - 5 = 1/5(x-20)
5(y-5) = x-20
5y-25 = x-20
5y-x = -20+25
5y-x = 5
The required equation is 5y-x = 5
