Answer: the point (3.667, 0.8)
Step-by-step explanation:
We want to find the point at which the lines:
h(x) = -(3/5)*x + (7/5)
and
k(x) = (-8/3)*x + (404/45)
If the lines intersect, then we must have:
h(x) = k(x)
if we write the functions we get:
-(3/5)*x + (7/5) = (-8/3)*x + (404/45)
Now we need to solve this for x.
-(3/5)*x + (8/3)*x = (404/45) - (7/5)
(8/3 - 3/5)*x = 404/45 - 63/45 = 341/45
(40/15 - 9/15)*x = 341/45
(31/15)*x = 341/45
x = (341/45)*(15/31) = 3.667
Now we can input this value of x in the functions to get the output.
h(3.667) = -(3/5)*3.667 + 7/5 = -0.8
Then the point where our points intersect is the point (3.667, 0.8)
