Question

Write a linear function from the given values:

f(2)=-2, f(1)=1


f(4)=1, f(8)=4

Answer 1

The slope-intercept form:

`y=mx+b`

m - slope

b - y-intercept

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have:

`f(2)=-2\to(2,\ -2)\\f(1)=1\to(1,\ 1)`.

Substitute:

`m=(1-(-2))/(1-2)=(3)/(-1)=-3`

Therefore we have
`y=-3x+b`.

Substitute the coordinates of the point (1, 1) to the equation:

`1=-3(1)+b`

`1=-3+b` add 3 to both sides

`4=b\to b=4`

Answer: y = -3x + 4

We have:

`f(4)=1\to(4,\ 1)\\f(8)=4\to(8,\ 4)`

Substitute:

`m=(4-1)/(8-4)=(3)/(4)`

Therefore we have
`y=(3)/(4)x+b`.

Substitute the coordinates of the point (4, 1) to the equation:

`1=(3)/(4)(4)+b`

`1=3+b` subtract 3 from both sides

`-2=b\to b=-2`

Answer:
`y=(3)/(4)x-2`