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:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have:

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

Substitute:

$m=\dfrac{1-(-2)}{1-2}=\dfrac{3}{-1}=-3$

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:

$m=\dfrac{4-1}{8-4}=\dfrac{3}{4}$

Therefore we have $y=\dfrac{3}{4}x+b$.

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

$1=\dfrac{3}{4}(4)+b$

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

$-2=b\to b=-2$

Answer: $y=\dfrac{3}{4}x-2$