Question

Help me find the parent function of this table pls

Answer 1

Linear Modeling

Any given situation is subject to be modeled as a linear function if the data follows the equation:

y = mx + b

Where m is the slope of the line represented by the dataset.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

`\displaystyle m=(y_2-y_1)/(x_2-x_1)`

Let's pick two points from the table. For example, (5,2) and (7,4). The slope is:

`\displaystyle m=(4-2)/(7-5)=(2)/(2)=1`

Now pick two other pair of points: (9,6) and (13,10):

`\displaystyle m=(10-6)/(13-9)=(4)/(4)=1`

Regardless of the points we select, the slope is always 1, thus the table represents a linear model.

To find the model, we use the value of the slope:

y = x + b

Now we replace any of the given points, for example (11,8):

8 = 11 + b

Solving: b = -3

Thus the equation of the line is:

y = x - 3

The parent function of a line is y=x