Question

Help please!!!!! Thank you

Answer 1

C

Explanation:

So we know that:

`f(3)=-2\text{ and } f(4)=-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=(y_2-y_1)/(x_2-x_1)`

Substitute (3,-2) for x₁ and y₁ and let (4,-4) be x₂ and y₂:

`m=(-4--2)/(4-3)`

Simplify:

`m=-2/1=-2`

So our slope is -2.

Now, use the point-slope form:

`y-y_1=m(x-x_1)`

Let's use (3,-2) for x₁ and y₁ and use -2 for m:

`y+2=-2(x-3)`

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)`

Simplify and distribute the right:

`2=-2x+6`

Subtract 6:

`-4=-2x`

Divide both sides by -2:

`x=2`

So, our x-intercept is (2,0)