Question

Which equation represents the line that passes through the points (–3, 7) and (9, –1)?

y = negative two-thirds x + 5
y = negative two-thirds x minus 7
y = two-thirds x minus 7
y = two-thirds x + 5

Answer 1

1st option

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 =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 3, 7) and (x₂, y₂ ) = (9, - 1)

m =
`(-1-7)/(9-(-3))` =
`(-8)/(9+3)` =
`(-8)/(12)` = -
`(2)/(3)` , then

y = -
`(2)/(3)` x + c ← is the partial equation

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

Using (9, - 1 ) , then

- 1 = - 6 + c ⇒ c = - 1 + 6 = 5

y = -
`(2)/(3)` x + 5 ← equation of line