FIRST METHOD
Answer:
Step-by-step explanation:
Given the table
x y
7 16
9 17
Missing x 18
13 Missing y
From the table, it is clear that y-values are incremented by 1 unit and the x-values are incremented by 2 units.
i.e.
y = 17-16 = 1
y = 18-17 = 1
as 19-18 = 1
Thus,
Thus, the value of Missing y = 19
also the x-values increment by 2.
i.e.
x = 9-7 = 2
as x = 11 - 9 = 2
Thus, Missing x = 11
Therefore,
2ND METHOD
Given that the table represents a linear function, so the function is a straight line.
Taking two points
Finding the slope between (7, 16) and (9, 17)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(7,\:16\right),\:\left(x_2,\:y_2\right)=\left(9,\:17\right)[/tex]
[tex]m=\frac{17-16}{9-7}[/tex]
[tex]m=\frac{1}{2}[/tex]
Using the point-slope form to determine the linear equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = 1/2 and the point (7, 16)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-16=\frac{1}{2}\left(x-7\right)[/tex]
Add 16 to both sides
[tex]y-16+16=\frac{1}{2}\left(x-7\right)+16[/tex]
[tex]y=\frac{1}{2}x+\frac{25}{2}[/tex]
Thus, the equation of the linear equation is:
[tex]y=\frac{1}{2}x+\frac{25}{2}[/tex]
Now substituting y = 18 in the equation
[tex]18=\frac{1}{2}x+\frac{25}{2}[/tex]
Switch sides
[tex]\frac{1}{2}x+\frac{25}{2}=18[/tex]
subtract 25/2 from both sides
[tex]\frac{1}{2}x+\frac{25}{2}-\frac{25}{2}=18-\frac{25}{2}[/tex]
[tex]\frac{1}{2}x=\frac{11}{2}[/tex]
[tex]x=11[/tex]
Thus, the value of missing x = 11 when y = 18
Now substituting x = 13 in the equation
[tex]y=\frac{1}{2}\left(13\right)+\frac{25}{2}[/tex]
[tex]y=\frac{13}{2}+\frac{25}{2}[/tex]
[tex]y=\frac{13+25}{2}[/tex]
[tex]y=\frac{38}{2}[/tex]
[tex]y = 19[/tex]
Thus, the value of missing y = 19 when x = 13
Hence, we conclude that:
- The value of missing x = 11
- The value of missing y = 19
Hence, option D is true.
