Which of the following ordered pairs could be placed in the table below and still have the relation qualify as a linear function? Input (x) Output (y) −5 7 −3 15 −1 23 ? ? (0, 31) (−7, 30) (1, 31) (0, −1)

y increases by 8 as x increases by 2 so the relationship is linear with slope 4. That is y=4x+c and 7=-20+c, so c=27.
The relationship seems to be y=4x+27. The only point to fit this equation is (1,31), Answer 3

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erinna erinna · Answer 2 · 2019-06-20T07:59:27+02:00

Answer:

The correct option is 3.

Step-by-step explanation:

If a linear function passing through two point, then the equation of linear function is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

From the given table it is clear that the function passing through the points (-5,7), (-3,15) and (-1,23).

Consider any two points from them, i.e., (-3,15) and (-1,23). So, the equation of line is

[tex]y-15=\frac{23-15}{-1-(-3)}(x-(-3))[/tex]

[tex]y-15=\frac{8}{2}(x+3)[/tex]

[tex]y-15=4(x+3)[/tex]

[tex]y-15=4x+12[/tex]

[tex]y=4x+12+15[/tex]

[tex]y=4x+27[/tex]

The equation of line is y=4x+27.

At x=0,

[tex]y=4(0)+27=27[/tex]

At x=-7,

[tex]y=4(-7)+27=-1[/tex]

At x=1,

[tex]y=4(1)+27=31[/tex]

Only point (1,31) is satisfy the equation of line. Therefore the ordered pairs (1,31) could be placed in the table below and still have the relation qualify as a linear function.

Hence option 3 is correct.