10. Write a rule for the function represented by the table.

Answer:

C) y=13+15x

Step-by-step explanation:

y=13+15x

The rule for the function represented by the table is: y = 15x + 13

Hence the correct option is A.

Given is a table showing the values of x and y:

x = 0, 1, 2, 3

y = 13, 28, 43, 58

Using this table we need to write a rule for the function represented by the table.

To determine a rule for the function represented by the table, let's examine the relationship between the values of x and y.

We notice that as x increases by 1, y increases by 15.

Based on this observation, we can create a linear equation to represent the relationship between x and y.

The equation will have the form:

y = mx + b

Where m is the slope of the line and b is the y-intercept.

To find the slope (m), we can calculate the difference in y-values divided by the difference in x-values:

m = (y₂ - y₁) / (x₂ - x₁)

Using the first two data points from the table (x₁ = 0, y₁ = 13 and x₂ = 1, y₂ = 28):

m = (28 - 13) / (1 - 0)

= 15 / 1

= 15

So, the slope of the line is 15.

To find the y-intercept (b), we can substitute the values of x and y from one of the data points into the equation and solve for b.

Let's use the first data point (x = 0, y = 13):

13 = 15(0) + b

13 = b

So, the y-intercept is 13.

Putting it all together, the rule for the function represented by the table is:

y = 15x + 13

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