Choose the equation of the line in slope-intercept form. Perpendicular to y = 2x + 9 and has the point (4,-1).

A. y = 2x + 3
B. y = 2x + 9
C. y = -1/2x + 1
D. y = -1/2x + 3

c. y = -1/2x + 1

steps-explanation:

given sample equation:

comparing to the formula of slope intercept form: y = mx + b

                                              [ where m is the slope and b is the y-intercept ]

we can determine here that the slope is 2 and 9 is the y-intercept.

but here we need only the slope.

making the slope perpendicular using: -1/m → 1/-2 → -1/2

formula:                  

using the formula:                     [ here known that y1 is -1 and x1 is 4 ]

C)    y = -1/2x + 1

Step-by-step explanation:

Equation of a line in slope-intercept form:  y = mx + b

(where m is the slope (gradient) and b is the y-intercept)

The slopes of two perpendicular lines are negative reciprocals of each other.  So, if the line is perpendicular to y = 2x + 9, then the slope m of the new line will be -1/2.

Therefore, y = -(1/2)x + b

We are told that the line passes through point (4, -1).  

Substituting the found value for m the the point (4, -1) into point-slope form:

y - y1 = m(x - x1)

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

y = -(1/2)x + 1

except a rational number. : )