(1) Required function is Β
. (2) Slope of line is
.
Step-by-step explanation:
1)
The function passing through (-3,9), (-1,3), (0,0) and (3,-9).
From these points it is noticed that the value of function decrease by 6 if the value of x increases by 2 and y-intercept is (0,0).
![m=\frac{\text{change in y}}{\text{change in x}}=\frac{-6}{2}=-3](/tpl/images/0248/7918/c3a1e.png)
Slope intercept of a line is
![y=mx+b](/tpl/images/0248/7918/904ac.png)
Where, m is slope and b is y-intercept.
So, function is defined as
![y=-3x+0](/tpl/images/0248/7918/2eaa7.png)
![y=-3x](/tpl/images/0248/7918/91d33.png)
The required function is Β
.
2)
It is given that the line joining two points (10, 9) and (40, 3).
Slope of line is
![m=\frac{y_2-y_1}{x_2-x_1}](/tpl/images/0248/7918/ab87e.png)
![m=\frac{3-9}{40-10}=\frac{-6}{30}=-\frac{1}{5}](/tpl/images/0248/7918/b8a8a.png)
Therefore slope of line is
.