Question

15 points!! Please help! please explain how you got you answers

Answer 1

We observe that a line will pass through 3 points, but to find a slope we only need two.

We see that it passes through points (assuming the scale of graph is 1 : 1) $P_1(x_1,y_1)=P_1(0,1)$ and $P_2(x_2,y_2)=P_2(2,-1)$.

We can use slope formula that applies for any line and produce the same slope for any two different points on the line

$m=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-1}{2-0}=-1$

So the slope is -1 also it intersects y-axis at $n=1$ so the general form of the linear function is

$f(x)=mx+n$

That is in your case

$\boxed{f(x)=-x+1}$

Hope this helps.