Question

Identity Structure find the rule for each function table.

Answer 1

Answer:

y  = 4x-1

Step-by-step explanation:

We have given a table of values in which x and y are given.

We have to find the rule for function.

y  = mx+c is equation in which m is slope and c is y-intercept.

slope  = m  =  y₂-y₁ / x₂-x₁

Putting given values in above formula, we have

slope  = m =  7-3 / 2-1

m  =  4 / 1

m  =  4

y  =  4x+c           eq(1)

Now, putting x  = 3 and y = 11 in above formula, we have

11  =  4(3)+c

11  = 12+c

c  = -1

putting value of c in eq(1), we have

y  =  4x-1 is equation of function whose values are given.

Answer 2

Answer:

The rule for given table is y = 4x - 1.

Step-by-step explanation:

From the given table it is noticed that the function passing through the points (1,3), (2,7) and (3,11).

If a line passing through the two points, then the equation of line is

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

The equation of line is

$y-3=\frac{7-3}{2-1}(x-1)$

$y-3=\frac{4}{1}(x-1)$

$y-3=4(x-1)$

$y-3=4x-4$

Add 3 both sides.

$y=4x-4+3$

$y=4x-1$

Therefore the rule for given table is y = 4x - 1.