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

b.) x + 4y = 7

Explanation:

when x = -1 and y = 2 : -1+4(2) = -1 +8 = 7 .....right

when x = 3 and y = 1 : 3+4(1) = 7 .....right

Answer 2

b

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (3, 1)

m =
`(1-2)/(3+1)` = -
`(1)/(4)`, thus

y = -
`(1)/(4)` x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 1, 2), then

2 =
`(1)/(4)` + c ⇒ c = 2 -
`(1)/(4)` =
`(7)/(4)`

y = -
`(1)/(4)` x +
`(7)/(4)` ← in point- slope form

Multiply through by 4

4y = - x + 7 ( add x to both sides )

x + 4y = 7 → b