Question

Write an equation of the line that passes through a pair of points : (- 5, - 2) (4 , 5) a. y = 7/9 x - 17/9 b. y = 7/9 x - 9/17 c. y = 7/9 x +17/9 d. y = - 7/9 x + 17/9

Answer 1

c

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) )`

let (x₁, y₁ ) = (- 5, - 2 ) and (x₂, y₂ ) = (4, 5 )

substitute these values into the formula for m

m =
`(5-(-2))/(4-(-5))` =
`(5+2)/(4+5)` =
`(7)/(9)` , then

y =
`(7)/(9)` x + c ← is the partial equation

to find c , substitute either of the 2 points into the partial equation

using (4, 5 )

5 =
`(7)/(9)` (4) + c =
`(28)/(9)` + c ( subtract
`(28)/(9)` from both sides )

`(45)/(9)` -
`(28)/(9)` = c , that is

c =
`(17)/(9)`

y =
`(7)/(9)` x +
`(17)/(9)` ← equation of line