Write the slope intercept forms of the equations of the lines through the given point that is a) parallel to the given line and b) perpendicular to the given line: (2/5,-1), 3x -2y=6

It can be handy to start with a version of the point-slope form of the equation for a line. For a line of slope m through point (h, k), an equation can be written as

... y = m(x -h) +k

The given line can be solved for y to get

... y = (3x -6)/2

Then the slope is the x-coefficient, 3/2.

The parallel line through (2/5, -1) will have the same slope, so its equation can be written

... y = (3/2)(x -2/5) -1

... y = (3/2)x -8/5 . . . . parallel line

The perpendicular line will have a slope that is the negative reciprocal of 3/2, that is, -2/3. Its equation can be written as

... y = (-2/3)(x -2/5) -1

... y = (-2/3)x -11/15 . . . . perpendicular line

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!