Question

F(-5) = 2,ƒ(7) = - 4
Please help

Answer 1

f(x) = -
`(1)/(2)` x -
`(1)/(2)`

Explanation:

the equation of a line in slope- intercept form is

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

given f(- 5) = 2, that is when x = - 5 , y = 2

f(7) = - 4, that is x = 7, y = - 4

the 2points (- 5, 2 ) and (7, - 4 ) lie on the line

calculate m using the slope formula

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

with (x₁, y₁ ) = (- 5, 2 ) and (x₂, y₂ ) = (7, - 4 )

m =
`(-4-2)/(7-(-5))` =
`(-6)/(7+5)` =
`(-6)/(12)` = -
`(1)/(2)` , then

f(x) = -
`(1)/(2)` x + c ← is the partial equation of the line

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

using (- 5, 2 ) , then

2 = -
`(1)/(2)` (- 5) + c =
`(5)/(2)` + c ( subtract
`(5)/(2)` from both sides )

-
`(1)/(2)` = c

f(x) = -
`(1)/(2)` x -
`(1)/(2)` ← equation of line