What is the equation of the line perpendicular to y=1/2x+6 that passes through the point (4, 1)?
a y=-2x+9
b y=-1/2x+3
c y=1/2x-1
dy=2x-7

A

Step-by-step explanation:

Find the slope of the perpendicular line.

The slopes are related by the formula

m1 * m2 = - 1

Since m1 is 1/2, m2 must be -2

So far what you have is y = -2x + b

Find the y intercept (b).

The new line goes through (4,1)

x = 4

y = 1

1 = -2(4) + b

1 = - 8 + b  

b = 1 + 8

b = 9

The answer is

y = - 2x + 9

Step-by-step explanation:

The slope-intercept form of an equation of a line:

m - slope

b - y-intercept

Let  

then

We have the equation of the line:

therefore a slope of a line perpendicular to given line has the slope:

Put the value of slope m = -2 and the coordinates of the point (4, 1) to the equation of a line:

          add 8 to both sides

Finally:

30

step-by-step explanation:

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