find the points of intersection of f(x)=3x-5 and g(x)=-4+9

To find the points of intersection between the functions f(x) = 3x - 5 and g(x) = -4 + 9, we need to set the two functions equal to each other and solve for x.

Set 3x - 5 = -4 + 9:

3x - 5 = 5

Next, add 5 to both sides of the equation:

3x = 10

To isolate x, divide both sides of the equation by 3:

x = 10/3

So the value of x at the point of intersection is 10/3.

To find the corresponding y-coordinate, substitute the value of x back into either of the original functions. Let's use f(x) = 3x - 5:

f(10/3) = 3(10/3) - 5

f(10/3) = 10 - 5

f(10/3) = 5

Hence, the point of intersection between f(x) = 3x - 5 and g(x) = -4 + 9 is (10/3, 5).