Answer:
(-3, 0)
Step-by-step explanation:
We are given two linear functions:
[tex]k(x)=4x+12\text{ and } f(x)=x+3[/tex]
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:
[tex]k(x)=f(x)[/tex]
Substitute:
[tex]4x+12=x+3[/tex]
Solve for x. Subtracting x from both sides yields:
[tex]3x+12=3[/tex]
And subtracting 12 from both sides yields:
[tex]3x=-9[/tex]
Thus, the x-coordinate of the point where the two lines intersect is:
[tex]x=-3[/tex]
To find the y-value, we can use either function. Using the second function, we acquire:
[tex]f(-3)=(-3)+3=0[/tex]
(You will obtain the same result if you use the first function. Try it!)
Thus, the point of intersection is (-3, 0).
