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Determine any data values that are missing from the table, assuming that the data represent a linear function.

a. Missing x:13 Missing y:20
b. Missing x:13 Missing y:19
c. Missing x:11 Missing y:20
d. Missing x:11 Missing y:19​

Determine Any Data Values That Are Missing From The Table Assuming That The Data Represent A Linear Functiona Missing X13 Missing Y20 B Missing X13 Missing Y19 class=

Sagot :

Mhanifaidn

Answer:

  • d. Missing x:11 Missing y:19​

Step-by-step explanation:

It can be determined that the function is:

  • y = 0.5x + 12.5

So missing x is:

  • 18 = 0.5x + 12.5 ⇒ 0.5x = 5.5 ⇒ x = 11

Missing y is:

  • y = 13*0.5 + 12.5 = 19

Missing numbers are:

  • x= 11 and y = 19

Correct choice is d.

Absor201idn

                                           FIRST METHOD

Answer:

  • Missing x = 11
  • Missing y = 19          

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,

  • Missing x = 11
  • Missing y = 19        

                                                2ND METHOD

Given that the table represents a  linear function, so the function is a straight line.

Taking two points

  • (7, 16)
  • (9, 17)

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.

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