Answer:
To find a linear function f, given f(15) = -2 and f(-5) = -10, we can use the slope-intercept form of a linear function, which is given by the equation y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope of the function. The slope (m) is calculated by taking the difference in the y-values and dividing it by the difference in the x-values between any two points on the line. In this case, we can use the points (15, -2) and (-5, -10):
m = (y2 - y1) / (x2 - x1)
= (-10 - (-2)) / (-5 - 15)
= (-10 + 2) / (-5 - 15)
= -8 / (-20)
= 2 / 5
Now that we have the slope (m), we can use either of the given points to find the y-intercept (b). Let's use the point (15, -2):
-2 = (2/5)(15) + b
-2 = 6 + b
b = -2 - 6
b = -8
Therefore, the linear function f(x) is given by:
f(x) = (2/5)x - 8
To find f(0), we substitute x = 0 into the equation:
f(0) = (2/5)(0) - 8
= 0 - 8
= -8
Therefore, f(0) = -8.
Step-by-step explanation: Hope this helps have a good day!