Given that D( x ) = 2 x , select all of the following that are true statements. D( x ) is a direct variation.
D( x ) is a function.
D( x ) is a rule for the set of points (5, 10), (6, 12) and (-2, -4).
x is the dependent variable.
D(6) = 3

D(x) is a function. TRUE. It is a function of x.

x is the dependent variable. FALSE. x is the independent variable because the function is expressed in terms of the independent variable.

D(6) = 3. FALSE. D(6) = 2(6) = 12. D(6) should be equal to 12.

D(x) is a direct variation. TRUE. This holds true to the definition of direct variation where one variable is related to the other variable at the same constant multple. In this case, it is 2.

D(x) is a rule for the set of points (5, 10), (6, 12) and (-2, -4). TRUE. If you replace x with the first coordinate, the function would be equal to the corresponding second coordinate.

Step-by-step explanation:

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.