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F(-5) = 2,ƒ(7) = - 4
Please help

User Anthony D
by
8.3k points

1 Answer

4 votes

Answer:

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

User Veturi
by
9.0k points

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