Answer:
C
Step-by-step explanation:
So we know that:
[tex]f(3)=-2\text{ and } f(4)=-4[/tex]
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:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute (3,-2) for x₁ and y₁ and let (4,-4) be x₂ and y₂:
[tex]m=\frac{-4--2}{4-3}[/tex]
Simplify:
[tex]m=-2/1=-2[/tex]
So our slope is -2.
Now, use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Let's use (3,-2) for x₁ and y₁ and use -2 for m:
[tex]y+2=-2(x-3)[/tex]
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:
[tex]0+2=-2(x-3)[/tex]
Simplify and distribute the right:
[tex]2=-2x+6[/tex]
Subtract 6:
[tex]-4=-2x[/tex]
Divide both sides by -2:
[tex]x=2[/tex]
So, our x-intercept is (2,0)
