Answer:
(-3, 0)
Step-by-step explanation:
We are given two linear functions:
![k(x)=4x+12\text{ and } f(x)=x+3](https://tex.z-dn.net/?f=k%28x%29%3D4x%2B12%5Ctext%7B%20and%20%7D%20f%28x%29%3Dx%2B3)
And we want to find the point at which the two lines intersect.
At the point the two lines intersect, their y-values will be the same. In other words, we can set their functions equal to each other and solve for x. Thus:
![k(x)=f(x)](https://tex.z-dn.net/?f=k%28x%29%3Df%28x%29)
Substitute:
![4x+12=x+3](https://tex.z-dn.net/?f=4x%2B12%3Dx%2B3)
Solve for x. Subtracting x from both sides yields:
![3x+12=3](https://tex.z-dn.net/?f=3x%2B12%3D3)
And subtracting 12 from both sides yields:
![3x=-9](https://tex.z-dn.net/?f=3x%3D-9)
Thus, the x-coordinate of the point where the two lines intersect is:
![x=-3](https://tex.z-dn.net/?f=x%3D-3)
To find the y-value, we can use either function. Using the second function, we acquire:
![f(-3)=(-3)+3=0](https://tex.z-dn.net/?f=f%28-3%29%3D%28-3%29%2B3%3D0)
(You will obtain the same result if you use the first function. Try it!)
Thus, the point of intersection is (-3, 0).