The line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0

y = -x/2 + 1

Step-by-step explanation:

Step 1: find the slope

2x - y - 7 = 0

2x - 7 = y

y = 2x - 7

Equation of a line is y = mx + c

m = slope

m = 2

Note: if two lines are perpendicular to the other, both lines are negative reciprocal of each other

Therefore m = -1/2

Step 2: using a point slope form

y - y1 = m( x - x1)

( 4 , -1)

x = 4

y = -1

y - (-1) = -1/2(x - 4)

y + 1 = -1/2(x - 4)

Open the bracket

y + 1 = -x + 4 / 2

y = (-x + 4) / 2 - 1

LCM = 2

y = -x + 4 - 2 / 2

y = (-x + 2)/2

Separate the two, so as to get the slope and the intercept

y = -x/2 + 2/2

y = -x/2 + 1

The equation of the line is

y = -x/2 + 1

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: