Linear function f (x) = x is graphed on a coordinate plane. The graph of a new line is formed by changing the slope of the original line to 2/3 and the y-intercept to 4. Which statement about the relationship between these two graphs is true? a. The graph of the new line is steeper than the graph of the original line, and the y-intercept has been translated down. b. The graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up. c. The graph of the new line is steeper than the graph of the original line, and the y-intercept has been translated up. d. The graph of the new line is less steep than the graph of the original line, and they-intercept has been translated down.

b. The graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up

Option b is right.

Step-by-step explanation:

Given that linear function f (x) = x is graphed on a coordinate plane.

The graph of a new line is formed by changing the slope of the original line to 2/3 and the y-intercept to 4.

The original slope was 1. Now changed to 2/3 i. e. slope is reduced. Hence the new line will be less steeper.

Also original line y = x has y intercept at the origin.

By changing y intercept to 4, we changed y intercept to upwards by 4 units.

Thus there is a vertical shift of 4 units.

b. The graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up

Option b is right.