A walking path across a park is represented by the equation y = -4x+10. A new path will be built perpendicular to this path. The paths will intersect at
the point (4.-6). Identify the equation that represents the new path.
102
10
10
O A. y -**-5
B. y --4x+10
C. y - 4x-22
O D. v-**-7

first invert fraction of the slope from 4/1 to 1/4 and switch sign. then figure out the y-intercept

the algebraic approach would work like this:

-4x + 10 = 1/4x + b

plug in what you got, here: the intersection information

-4*(4) + 10 = 1/4*(4) + b

-16 + 10 = 1 + b

-6 = 1 + b

-7 = b

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)