A linear function includes the ordered pairs (0, 1), (3, 3), and (9, n). What is the value of n?

The correct answer is: 7

Here , we have to find value of n.
Firstly, we have, three points on a linear function
(0,1) , (3, 3) and (9, n) .
So to find k , the slope between two points (3,4) and (5,5) is:
m = (y2 – y1) / (x2 – x1)
m = (3 –1) / ( 3 – 0) = 2 / 3
Now, we have slope between two points (0, 1) and (9, n) is:
m= (n – 1) / (9 – 0)
m= (n – 1) / 9
we know that the slope of two point in same line is same so , we have:
2 / 3 = (n – 1) / 9
Cross multiplication,
2 x 9 = 3 x (n – 1 )
18 = 3n – 3
Add both side by 3,
18 + 3 = 3n – 3 + 3
21 = 3n
Divide both side by 3 ,
n = 7
Therefore , the value of n is 7.
The correct answer is 7(option (c)).
Or,
If the function is linear, the slope has to be the same between any
2 points.
Using the first two points, the slope is
Therefore, using the next two points, the slope must also be ;
So, = ;
So, 3n –9=18–6
3n=12+9=21
n=7

In this question, we have to find the value of n in linear function, to find it we know the slope of two point in same line is same so, just find the slope between two different points and then find the compare both them equally and find the value of n.