Answer:
C
Step-by-step explanation:
So we know that:
![f(3)=-2\text{ and } f(4)=-4](https://tex.z-dn.net/?f=f%283%29%3D-2%5Ctext%7B%20and%20%7D%20f%284%29%3D-4)
This is the same as saying we have two coordinates: (3,-2) and (4,-4).
Let's find the equation of the linear function.
First, let's find the slope:
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Substitute (3,-2) for x₁ and y₁ and let (4,-4) be x₂ and y₂:
![m=\frac{-4--2}{4-3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-4--2%7D%7B4-3%7D)
Simplify:
![m=-2/1=-2](https://tex.z-dn.net/?f=m%3D-2%2F1%3D-2)
So our slope is -2.
Now, use the point-slope form:
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
Let's use (3,-2) for x₁ and y₁ and use -2 for m:
![y+2=-2(x-3)](https://tex.z-dn.net/?f=y%2B2%3D-2%28x-3%29)
Now, we can figure out the x-intercept.
Recall that the x-intercept is when the graph touches the x-axis.
In other words, the y-value would be 0. It will be (x,0).
So, to solve for the x-intercept, substitute 0 for y and solve for x:
![0+2=-2(x-3)](https://tex.z-dn.net/?f=0%2B2%3D-2%28x-3%29)
Simplify and distribute the right:
![2=-2x+6](https://tex.z-dn.net/?f=2%3D-2x%2B6)
Subtract 6:
![-4=-2x](https://tex.z-dn.net/?f=-4%3D-2x)
Divide both sides by -2:
![x=2](https://tex.z-dn.net/?f=x%3D2)
So, our x-intercept is (2,0)