Question

Identity Structure find the rule for each function table.

Answer 1

y = 4x-1

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

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

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=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The equation of line is

`y-3=(7-3)/(2-1)(x-1)`

`y-3=(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.