Question

Choose the equation that represents a line that passes through points (−1, 2) and (3, 1).

A. 4x − y = −6
B. x + 4y = 7
C. x − 4y = −9
D. 4x + y = 2

Answer 1

x + 4y = 7

Explanation:

Answer 2

B. x + 4y = 7

Explanation:

There are two points given:

(-1, 2) and (3, 1)

The standard form of equation is:

y = mx+b

We have to find the slope first

`m = (y_2-y_1)/(x_2-x_1) \\= (1-2)/(3+1)\\ = (-1)/(4)`

So,

y = (-1/4)x + b

We have to find the value of b

1 = (-1/4)(3) + b

1 = -(3/4) + b

1 + (3/4) = b

7/4 = b

Putting the values of b and m in standard equation

`y = -(1)/(4)x+(7)/(4)\\   Multiplying\ whole\ equation\ by\ 4\\4y = -x+7\\x+4y = 7`

Hence, option B. x + 4y = 7 is correct ..