Question

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)

Answer 1

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

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

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

$y-15=\frac{23-15}{-1-(-3)}(x-(-3))$

$y-15=\frac{8}{2}(x+3)$

$y-15=4(x+3)$

$y-15=4x+12$

$y=4x+12+15$

$y=4x+27$

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

At x=0,

$y=4(0)+27=27$

At x=-7,

$y=4(-7)+27=-1$

At x=1,

$y=4(1)+27=31$

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.

Answer 2

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