141,834 views
44 votes
44 votes
NO LINKS. Part 1: Complete the sequence​

NO LINKS. Part 1: Complete the sequence​-example-1
User Satpal Tanan
by
3.1k points

1 Answer

12 votes
12 votes

Answer:

a) (6, 6) and (7, 4)

b)
t(n)=-2n+18

c) see attached

Explanation:

From inspection of the table, we can see that as n increases by 2, t(n) decreases by 4. Therefore, as this a directly proportional relationship, it is a linear function.

So as n increases by 1, t(n) will decrease by 2.

Therefore, the remaining two ordered pairs are:

(6, 6)

(7, 4)

We know that the function decreases by 2 each time n increases by 1, so the slope (gradient) of the linear function will be -2.

Using the point-slope formula:
y-y_1=m(x-x_1)

(where
m is the slope and
(x_1,y_1) is a point on the line)

Given:


  • m=-2

  • (x_1,y_1)=(1,16)


\implies y-16=-2(x-1)


\implies y=-2x+18


\implies t(n)=-2n+18

Graphing

To find the y-intercept, substitute
n=0 into the equation:


\implies t(0)=-2(0)+18=18

Therefore, the y-intercept is (0, 18)

To find where the line crosses the x-axis, set the equation to zero and solve for n:


\implies -2n+18=0


\implies 2n=18


\implies n=9

Therefore, the line crosses the x-axis at (9, 0)

NO LINKS. Part 1: Complete the sequence​-example-1
User Leed
by
3.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.