Question

Please help me last question of my test and I don't understand

Answer 1

Answer:

f(x) = (-3/2)x-2

Step-by-step explanation:

I used the graph provided to answer the question. From the graph:

1. We can see that the slope is going down from left to right, so the number before "x" in the function must be negative

2. We can see that when x=0, f(x)=-2

3. We can see that when x=-2, f(x)=1

Remember that f(x) is just equal to the y-coordinate. The only function from the ones provided that fits the three observations above is the first one; f(x) = (-3/2)x-2.

Answer 2

Answer:

The answer is $f(x)=\frac{-3*x}{2}-2$.

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:

1. Find two coordanates points.
2. Find the slope of the line from the two points.
3. Choose any of the two points and replace in the formula.
4. Free the "y" variable.

$y-y_1=m*(x-x_1)$

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

Where:

m=slope of the linear function

$x_1=$Coordinate "x" of the first chosen point.

$y_1=$Coordinate "y" of the first chosen point.

$x_2=$Coordinate "x" of the second chosen point.

$y_2=$Coordinate "y" of the second chosen point.

In this case, we can choose two easy points:

$P_1=(-2,1)\\P_2=(0,-2)$

So,

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-1}{0-(-2)}=\frac{-3}{2}$

$y-y_1=m*(x-x_1)\\y-1=\frac{-3}{2}*(x-(-2))\\y=\frac{-3}{2}*(x+2)+1\\y=\frac{-3*x}{2}-3+1\\y=\frac{-3*x}{2}-2$

Finally, the answer is $f(x)=\frac{-3*x}{2}-2$.