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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

User Harini
by
8.5k points

2 Answers

1 vote

Answer:

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.

User Ahmed Gaber
by
7.3k points
2 votes

ANSWER

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

User Chaffelson
by
8.0k points

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