Question

Write the equation of a line that passes through (3.5,0) and is perpendicular to 8y+4x=64.

Answer 1

Answer:

y = 2x + 3.5

Step-by-step explanation:

Step 1: find the slope

8y + 4x = 64

8y = 64 - 4x

Make y the subject of the formula

y = (64 - 4x)/8

y = ( -4x + 64)/8

Separate to get slope

y = -4x/8 + 64/8

y = -x/2 + 8

Slope is the coefficient of x

m = -1/2

Note: if two lines are perpendicular to the other , it is negative reciprocal to each other

m = 2

Using the point slope form equation

y - y1 = m(x - x1)

y - y1 = 2(x - x1)

Substitute the point

( 3.5 , 0)

x1 = 3.5

y1 = 0

y - 3.5 = 2( x - 0)

open the bracket

y - 3.5 = 2x - 0

y = 2x - 0 + 3.5

y = 2x + 3.5

The equation of the line is

y = 2x + 3.5