Question

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

Answer 1

Answer:

value of n is 5

Third option is correct.

Step-by-step 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

$m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-10+25}{-1+4}\\\\m=\frac{15}{3}\\\\m=5$

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

Answer 2

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