Question

Find the equation of the line through the points (3, 6) and (-1, 1).

Answer 1

Answer:

D. y = 5/4x + 2 1/4

Step-by-step explanation:

The equation of the line is

y = mx + c

Step 1: find the slope

( 3 , 6) ( -1 , 1)

m = y2 - y1 / x2 - x1

m - is the slope of the line

( y1 , y2) - are point on the line

( x1, x2) - are point on the line

x1 = 3

y1 = 6

x2 = -1

y2 = 1

Inserting into the formula

m = y2 - y1 / x2 - x1

m = 1 - 6 / -1 - 3

m = -5/-4

Minus cancels minus

= 5/4

Step 2: substitute m into the equation of the line

y = mx + c

y = 5/4x + c

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

Let's pick ( 3 , 6)

x - 3

y - 6

y = 5/4x + c.

6 = 5/4(3) + c

6 = 5 * 3 / 4 + c

6 = 15/4 + c

c = 6 - 15/4

LCM = 4

c = 24 - 16 / 4

c = 9/4

c = 2 1/4

Step 4: sub c into the equation

y = 5/4x + c

y = 5/4x + 2 1/4

The equation of the line is

y = 5/4x + 2 1/4