Which of the following are characteristics of the graph of the linear parent function?

Option C and D are correct choices.

Step-by-step explanation:

We are asked to select the correct options of the given choices about the graph of a linear parent function.

Let us check our given choices one by one.

A. It has a slope of 2.

Since we know that equation of the linear parent function is and it has a slope of 1, therefore, option A is not a correct choice.

B. It goes through the origin.

Since we know that line  passes through the origin (0,0), therefore, option B is the correct choice.

C. It is a straight line.

Since rate of change of the linear parent function is always 1, therefore, it forms a straight line and option C is the correct choice.

D. It is in quadrants 1st and 3rd.

Since line lies in 1st and 3rd quadrants, therefore, option D is correct choice as well.