Item 11 Write a linear function f with f(−4)=2 and f(6)=−3.

Question

How do I write this into a function please explain steps

Answer 1

Item 11 Write a linear function f with f(−4)=2 and f(6)=−3.

Hi j.

for the rest of you life, if you have two points in the (x,y) coordinate system, a line can be drawn that connects them and extends with the same slope (the incline) past the points. It can always be put into equation form

by using the formula

m=(y minus y value point on line)/(x minus x value point on line that is paired with the y value on the line)

m is the first step, it is the slope. m=(y₂-y₁)//(x₂-x₁). For your problem the points are (-4,2) and (6,-3)

which point is chosen as (x₂,y₂) doesn't matter but x₂-x₁ being positive (x₂ is to right of x₁) is a logical choice.

for your problem m=(-3-2)/(6-(-4))=-(1/2) the line inclines down so as x increases y decreases at rate -(1/2) for every x.

as for the equation, either given point is on line so either will give correct answer

-(1/2)=(y-2)/(x-(-4) ;;;;;; you could leave in this form;;;;;;

will work out the same as

-(1/2)=(y-(-3))/(x-6)

to use algebra to find y as a function x , y=f(x)

either equation computes to y= -(1/2)x

which means the line goes though the origin (when x =0, y=0)

Answer 2

You are asked to find the equation of the line that passes through 2 points: (-4,2) and (6,-3).

f(-4)=2

x=-4

f(x)=y=2

f(6)=-3

x=6

f(x)=y=-3

1st step: Find the slope of the line

slope: m = change in y / change in x

m = (2 - (-3)) / ((-4) - 6)

m = 5 / -10

m = -1 / 2

2nd step: Put one of the given points and the slope into the "Point-Slop formula": y - y₁ = m (x - x₁)

y - 2 = -1/2 (x-(-4))

y - 2 = -1/2 (x+4)

y - 2 = -1/2x - 2

y = -1/2x - 2 + 2

y = -1/2x

Equation of the line that passes through (-4,2) and (6,-3): y = -1/2x

Answer 3

Hi

The functions f(-4) = 2 and f(6) = -3 are the value of y when x is equal to -4 and 6. So there is a proportional constant that relates x to y.

f(-4) = 2 is basically (-4)(?) = 2

? is a proportional constant

Isolate ? by dividing by -4

Then ? = ²/_-4 = -¹/₂

f(6) = 3 is basically (6)(?) = -3

Again, ? is a proportional constant

Isolate ? by dividing by 6

Then ? = -³/₆ = -¹/₂

So... the linear function is f(x) = -¹/₂(x)

Hope this helps :)