Question

If f(x) is a linear function, what is the value of n?

Answer 1

m = (-10 + 25)/(-1 + 4) = 15/3 = 5

so

5 = (20 + 10)/(n + 1)

5(n+1) = 30

5n + 5 = 30

5n = 25

n = 5

Answer

n = 5

Answer 2

value of n is 5

Third option is correct.

Explanation:

Let the equation of the linear function is y = mx + b

From the given table, we have two points (-4,-25) and (-1,-10)

The slope of the line containing these two points is

`m=(y_2-y_1)/(x_2-x_1)\\\\m=(-10+25)/(-1+4)\\\\m=(15)/(3)\\\\m=5`

Now, put m = 5, x = -4 and y = -25 in the equation y = mx+b

`-25=5\cdot(-4)+b\\\\-25=-20+b\\\\b = -5`

Therefore, equation of linear function is
`y=5x-5`

Now, put x = n and y =20

`20=5n-5\\\\5n=25\\\\n=5`

Therefore, the value of n is 5