The value of the function f(x)
is -7 when x is 4 and -13 when x is -6. The value of the function g(x)
is 17 when x is -3 and is -3 when x is 5. If p represents the slope of f(x)
and q represents the slope of g(x)
, what is the value of pq?(1 point)
Responses
32
3 halves
23
2 thirds
−23
negative 2 thirds
−32
To find the slope of a function, we can use the formula:
slope = (change in y) / (change in x)
For the function f(x), we have:
slope of f(x) = (f(-6) - f(4)) / (-6 - 4)
= (-13 - (-7)) / (-10)
= (-13 + 7) / (-10)
= -6 / -10
= 3/5
For the function g(x), we have:
slope of g(x) = (g(5) - g(-3)) / (5 - (-3))
= (-3 - 17) / (5 + 3)
= (-20) / (8)
= -5/2
Now, to find the value of pq, we multiply the slopes of f(x) and g(x):
pq = (3/5) * (-5/2)
= (-15/10) * (1/2)
= -15/20
= -3/4
Therefore, the value of pq is -3/4.