In this question , we have a graph given, and we have to find the x coordinate of the intersection point .
From the graph , the input value is approximately 3.3 .
In the graph,
![f(x) =3](https://tex.z-dn.net/?f=%20f%28x%29%20%3D3%20)
And for g(x), we need the slope and y intercept .
Slope is the ratio of rise and run .
Here rise equals 3 units and run equals 2 units. And the graph touch the y axis at -2 .
So the equation of g(x) is
![g(x) = \frac{3}{2}x -2](https://tex.z-dn.net/?f=%20g%28x%29%20%3D%20%5Cfrac%7B3%7D%7B2%7Dx%20-2%20)
We need to do
![f(x)= g(x)](https://tex.z-dn.net/?f=%20f%28x%29%3D%20g%28x%29%20)
Substituting the values of the two functions, we will get
![3 = \frac{3}{2}x -2](https://tex.z-dn.net/?f=%203%20%3D%20%5Cfrac%7B3%7D%7B2%7Dx%20-2%20)
Adding 2 to both sides
![5 = \frac{3}{2}x](https://tex.z-dn.net/?f=%205%20%3D%20%5Cfrac%7B3%7D%7B2%7Dx%20)
Cross multiplication
![10 =3x \\ x = \frac{10}{3}](https://tex.z-dn.net/?f=%2010%20%3D3x%0A%5C%5C%0Ax%20%3D%20%5Cfrac%7B10%7D%7B3%7D%20)
![x = 3.3](https://tex.z-dn.net/?f=%20x%20%3D%203.3%20)
So the input value is 3.3 approx