Which equation in point-slope form describes the line that passes through the point (4,-5) and is perpendicular to the line represented by - 7x + 2y = 14?

y = -2/7x - 27/7

Step-by-step explanation:

first find the slope of the line -7x + 2y = 14 by solving for 'y'

2y = 7x + 14

y = 7/2x + 7

since the slope is 7/2 then the line that is perpendicular will need the opposite and reciprocal of 7/2 which is -2/7

knowing the slope ('m') and having the point (4, -5) we can find the y-intercept of the new line ('b')

y = mx + b

-5 = (-2/7)(4) + b

-5 = -8/7 + b

[change -5 into -35/7]

-35/7 + 8/7 = b

b = -27/7

put 'm' and 'b' into y = mx + b

y = -2/7x - 27/7