Answer:
(1) Required function is [tex]y=-3x[/tex] . (2) Slope of line is [tex]-\frac{1}{5}[/tex] .
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).
[tex]m=\frac{\text{change in y}}{\text{change in x}}=\frac{-6}{2}=-3[/tex]
Slope intercept of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
So, function is defined as
[tex]y=-3x+0[/tex]
[tex]y=-3x[/tex]
The required function is [tex]y=-3x[/tex] .
2)
It is given that the line joining two points (10, 9) and (40, 3).
Slope of line is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{3-9}{40-10}=\frac{-6}{30}=-\frac{1}{5}[/tex]
Therefore slope of line is [tex]-\frac{1}{5}[/tex] .
