Question

A linear function includes the ordered pairs (2,5), (6,7) and (k,11). What is the value of k?

A)8
B)10
C)12
D)14

Answer 1

Option D will be the answer.

Explanation:

y intercept form of a line is represented by y = mx + c

Where m = slope of the line and c = y- intercept of the line.

A line passing through two points (2, 5) and ( 6, 7) has the slope

m =
`(y-y')/(x-x')`

=
`(7-5)/(6-2)`

=
`(2)/(4)`

=
`(1)/(2)`

Equation will be y =
`(x)/(2)+c`

This line passes through (2, 5)

5 =
`(1)/(2)* 2+c`

c = 5 - 1

c = 4

And the equation will be y =
`(1)/(2)x+4`

Since a point (k 11) passes through the line then we will plug in these values in the equation to find the value of k.

11 =
`(1)/(2)* k+4`

11 - 4 =
`(k)/(2)`

7 =
`(k)/(2)`

k = 2×7

= 14

Option D will be the answer.

Answer 2

D)14

EXPLANATION

The linear function includes the ordered pairs (2,5), (6,7) and (k,11).

The slope of this line is the same for any two given points:

`(7 - 5)/(6 - 2) = (11 - 7)/(k - 6)`

`(2)/(4) = (4)/(k - 6)`

Cross multiply,.

2(k-6)=4×4

2(k-6)=16

Divide both sides by 2

k-6=8

k=8+6

k=14