Question

NO LINKS. Part 1: Complete the sequence​

Answer 1

Answer:

a)  (6, 6)  and  (7, 4)

b)  $t(n)=-2n+18$

c)  see attached

Step-by-step 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)