Question

If f(x) is a linear function, what is the value of n? x f(x) –4 –25 –1 –10 n 20

Answer 1

n = 5 is the answer to your question sir.

Answer 2

The value of n is 5.

Explanation:

We have been given that f(x) is a linear function and we are asked to find the value of n from the provided table.

x f(x)

-4 -25

-1 -10

n 20

First of all we will find the slope of the given using our given points (-4,-25) and (-1,-10) in slope formula.

`m=(y_2-y_1)/(x_2-x_1)`

Upon substituting coordinates of our given points we will get,

`m=(-10--25)/(-1--4)`

`m=(-10+25)/(-1+4)`

`m=(15)/(3)`

`m=5`

Since we know that the equation of a line in slope-intercept form is:
`y=mx+b`, where, m= Slope and b= y-intercept.

Upon substituting m = 5 in slope-intercept form of equation we will get,

`y=5x+b`

Now let us find y-intercept by substituting coordinates of one point in our given line.

`-10=5(-1)+b`

`-10=-5+b`

`-10+5=-5+5+b`

`-5=b`

So the equation of given line will be,

`y=5x-5`

Now let us find value of n by substituting x = n and y = 20 in our equation.

`20=5*n-5`

`20+5=5*n-5+5`

`25=5*n`

`(25)/(5)=(5*n)/(5)`

`5=n`

Therefore, the value of n is 5.