Question

Solve ​f(x)=​g(x). What are the points of intersection of the graphs of the two​ functions?

f(x)= -5x+10; g(x)=9x+14
If ​f(x) =​g(x),
The​ point(s) of intesection of the two graphs​ is/are:

Answer 1

To find the points of intersection of the graphs of two functions, set the two functions equal to each other and solve for x. The point of intersection is (12/7, 10/7).

Step-by-step explanation:

To find the points of intersection of the graphs of two functions, we can set the two functions equal to each other and solve for the value of x. In this case, we have:

-5x + 10 = 9x + 14

Adding 5x to both sides and subtracting 14 from both sides, we get:

24 = 14x'

Dividing both sides by 14, we find that x = 24/14 = 12/7.

To find the corresponding y-value, we can substitute this value of x into either of the original functions. Let's use f(x) = -5x + 10:

f(12/7) = -5(12/7) + 10 = -60/7 + 70/7 = 10/7.

Therefore, the point of intersection of the two graphs is (12/7, 10/7).