Write an equation for the linear function f satisfying the given conditions.
1) f(-1) = -5 and f(5) = 7

 f(x) = 2x - 3

We're given f(-1) = -5 and f(5) = 7

This means we know the two points (-1,-5) and (5,7) are on the line.

Find the slope

m = (y2-y1)/(x2-x1)

m = (7-(-5))/(5-(-1))

m = (7+5)/(5+1)

m = 12/6

m = 2

The slope is 2.

Use this along with (x1,y1) to find the equation. We'll use point slope form

y - y1 = m(x - x1)

y - (-5) = 2(x - (-1))

y + 5 = 2(x + 1)

y = 2x + 2 - 5

y = 2x - 3

f(x) = 2x - 3

huh? im pretty sure it is in 199

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

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

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form