Answer:
The answer is [tex]f(x)=\frac{-3*x}{2}-2[/tex].
Step-by-step explanation:
In order to determine the function, we have to know the formula to make a linear function from two points.
The "Point-Slope" formula is required to make linear function, where we have to follow the next steps:
- Find two coordanates points.
- Find the slope of the line from the two points.
- Choose any of the two points and replace in the formula.
- Free the "y" variable.
[tex]y-y_1=m*(x-x_1)[/tex]
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where:
m=slope of the linear function
[tex]x_1=[/tex]Coordinate "x" of the first chosen point.
[tex]y_1=[/tex]Coordinate "y" of the first chosen point.
[tex]x_2=[/tex]Coordinate "x" of the second chosen point.
[tex]y_2=[/tex]Coordinate "y" of the second chosen point.
In this case, we can choose two easy points:
[tex]P_1=(-2,1)\\P_2=(0,-2)[/tex]
So,
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-1}{0-(-2)}=\frac{-3}{2}[/tex]
[tex]y-y_1=m*(x-x_1)\\y-1=\frac{-3}{2}*(x-(-2))\\y=\frac{-3}{2}*(x+2)+1\\y=\frac{-3*x}{2}-3+1\\y=\frac{-3*x}{2}-2\\[/tex]
Finally, the answer is [tex]f(x)=\frac{-3*x}{2}-2[/tex].
