Question

Find the equation of the line that is perpendicular to the given line and passes through the given point. Enter your answer in slope-intercept form (y = mx + b) with the values of m and b given as decimals, rounded to the nearest hundredth if necessary.

y = 2x ; (4, −4)

Answer 1

y = -0.5x -2

Explanation:

if two lines are perpendicular, their product equals -1

_________________________________________

let the equation of required line be

y = mx + b as given in the problem to be slope intercept form

m = slope

given line

y = 2x

it is also in y = mx + b , comparing this with y =2x

m = 2 and b =0

now

as product of two perpendicular lines = -1

m*2 = -1

thus

m = -1/2 = -0.5

thus,

slope of required line is -0.5

in y = mx + b

m = -0.5

thus,

y = -0.5x + b

given that this line passes through(4,-4)

putting y = -4 and x = 4 in this equation we can find value of b

-4 = -0.5*4 + b

-4 = -2 + b

=> -4 + 2 = b

thus, b = -2

Thus, slope intercept form of equation is y = -0.5x -2