Question

The graph of f passes through (-4,7) and is perpendicular to the line that has

an x-intercept of 2 and a y-intercept of - 4.
The equation of the function is ?

Answer 1

f(x) = -
`(1)/(2)` x + 5

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 ) = (2, 0 ) , x- intercept and (x₂. y₂ ) = (0, - 4) , y- intercept

m =
`(-4-0)/(0-2)` =
`(-4)/(-2)` = 2

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(2)` , then

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

to find c substitute (- 4, 7 ) into the partial equation

7 = -
`(1)/(2)` (- 4) + c = 2 + c ( subtract 2 from both sides )

5 = c

y = f(x) = -
`(1)/(2)` x + 5 ← equation of function