Question

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

Options :
• 2
• 4
• 5
• 9​

Answer 1

Answer:

The value of n is 5.

Step-by-step 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=\frac{y_2-y_1}{x_2-x_1}m=

x

2

−x

1

y

2

−y

1

Upon substituting coordinates of our given points we will get,

m=\frac{-10--25}{-1--4}m=

−1−−4

−10−−25

m=\frac{-10+25}{-1+4}m=

−1+4

−10+25

m=\frac{15}{3}m=

3

15

m=5m=5

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

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

y=5x+by=5x+b

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

-10=5(-1)+b−10=5(−1)+b

-10=-5+b−10=−5+b

-10+5=-5+5+b−10+5=−5+5+b

-5=b−5=b

So the equation of given line will be,

y=5x-5y=5x−5

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

20=5*n-520=5∗n−5

20+5=5*n-5+520+5=5∗n−5+5

25=5*n25=5∗n

\frac{25}{5}=\frac{5*n}{5}

5

25

=

5

5∗n

5=n5=n

Therefore, the value of n is 5.

Answer 2

5




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