Question

write a linear function f with the given values. f(-10) = 4, f (8) = -5 Can someone please help me with this question​

Answer 1

Answer: y=-0.5x-1

Explanation:

y=mx+b

Convert the given values f(-10) = 4, f (8) = -5 to coordinates (-10,4) (8,-5)

Hence we use the formula for finding the slope m:

`\displaystyle\\\boxed{m=(y_2-y_1)/(x_2-x_1) }\\\\x_1=-1\ \ \ \ \ x_2=8\ \ \ \ \ \ y_1=4\ \ \ \ \ y_2=-5\\\\m=(-5-4)/(8-(-10))\\\\m=(-9)/(8+10) \\\\m=(-9)/(18) \\\\m=-0.5\\\\Thus, y=-0.5x+b\ \ \ \ (1)\\\\`

We substitute the value of (-10,4) into equation (1):

`4=-0.5(-10)+b\\\\4=5+b\\\\-1=b\\\\Thus, b=-1`

Hence, y=-0.5x-1