Question

A line passes through (2,-1) and (4,5). Which answer is the equation of the line?

Answer 1

`- 3x + y = - 7`

Option C is the correct option.

Explanation:

A line passes through ( 2 , -1 ) and ( 4 , 5 )

The equation of line:

`(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)`

Plug the values

`( y - ( - 1))/(x - 2) = (5 - ( - 1))/(4 - 2)`

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

`(y + 1)/(x - 2) = (5 + 1)/(4 - 2)`

Add the numbers

`(y + 1)/(x - 2) = (6)/(4 - 2)`

Subtract the numbers

`(y + 1)/(x - 2) = (6)/(2)`

Reduce the numbers with 2

`(y + 1)/(x - 2) = 3`

Apply cross product property

`3x - 6 = y + 1`

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

`3x - y = 1 + 6`

Add the numbers

`3x - y = 7`

`- 3x + y = - 7`

Hope this helps...

Best regards!

Answer 2

C.

Explanation:

Slope = m = (y2 - y1)/(x2 - x1) = (5-(-1))/(4 - 2) = 6/2 = 3

Slope - point form:

y - y1 = m(x -x1)

y - 5 = 3(x - 4)

y - 5 = 3x - 12

- 3x + y = - 12 + 5

- 3x + y = - 7