Find an equation of the line that passes through the points (-1/2,3/4) and (3/4,-1/2)

A. y=x+4
B. Y=-x+1/4
C. Y=5x-4/7
D. Y=-5x-7/4

B. y = -x + 1/4

Step-by-step explanation:

The equation of a line is

y = mx + c

step 1: find the slope

m = y2 - y1 / x2 - x1

Given two points

( -1/2 , 3/4) ( 3/4, -1/2)

x1 = -1/2

y1 = 3/4

x2 = 3/4

y2 = -1/2

Insert the values into the equation

m = ( -1/2 - 3/4) / ( 3/4 - (-1/2)

m = ( -1/2 - 3/4) / ( 3/4 + 1/2)

m = -5/4 / 5/4

m = -5/4 * 4/5

m = -5 * 4 / 4 * 5

= -20/20

= -1

Step 2: substitute m into the equation

y = mx + c

y = -1x + c

y = -x + c

Step 3: sub any of the two points given into the equation

Let's pick ( 3/4 , -1/2)

x = 3/4

y = -1/2

y = -x + c

-1/2 = -3/4 + c.

c = -1/2 + 3/4

LCM = 4

c = -2 + 3 / 4

= 1/4

y = -x + 1/4

The equation of the line is

y = -x + 1/4