Determine and state an equation of the line perpendicular to the line 8x + 6y = 15 and passing through the point (3,-4)

4y - 3x = -25

Step-by-step explanation:

The equation of a line in point-slope form is expressed as

y - y0 = m(x - x0)

(x0, y0) is the point

m is the slope

Given

(x0, y0) = (3, -4)

Also given the equation;

8x + 6y = 15

Rewrite in standard form;

6y = -8x+15

y = -8/6 x + 15/6

y = -4/3 x + 5/2

Slope m = -4/3

Since the required line is perpendicular to the given line =,

Slope = -1/(-4/3) = 3/4

Substitute into the formula;

y - (-4) = 3/4(x-3)

y + 4 = 3/4(x-3)

4(y+4) = 3(x-3)

4y + 16 = 3x - 9

4y - 3x = -9-16

4y - 3x = -25

This gives the required equation

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!

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explanation: