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:
[tex] \frac{7 - 5}{6 - 2} = \frac{11 - 7}{k - 6} [/tex]
[tex]\frac{2}{4} = \frac{4}{k - 6} [/tex]
Cross multiply,.
2(k-6)=4×4
2(k-6)=16
Divide both sides by 2
k-6=8
k=8+6
k=14
Answer:
Option D will be the answer.
Step-by-step 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 = [tex]\frac{y-y'}{x-x'}[/tex]
= [tex]\frac{7-5}{6-2}[/tex]
= [tex]\frac{2}{4}[/tex]
= [tex]\frac{1}{2}[/tex]
Equation will be y = [tex]\frac{x}{2}+c[/tex]
This line passes through (2, 5)
5 = [tex]\frac{1}{2}\times 2+c[/tex]
c = 5 - 1
c = 4
And the equation will be y = [tex]\frac{1}{2}x+4[/tex]
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 = [tex]\frac{1}{2}\times k+4[/tex]
11 - 4 = [tex]\frac{k}{2}[/tex]
7 = [tex]\frac{k}{2}[/tex]
k = 2×7
= 14
Option D will be the answer.
