1.The following table shows several ordered pairs of a function, m(x).

x m(x)

-1 -1.5

1 1.5

2 3

4 6

Graph m(x) on a coordinate plane to determine whether or not the function represents a direct variation. In complete sentences, describe your conclusion and reasoning. Include your graph in your answer.

2. What is the constant of proportionality in the direct variation represented on the following graph?

-1/4

1/4

-4

4

3. The perimeter of a square is directly proportional to the length of its sides.

A. Write an equation to represent this direct variation. Make sure to define your variables.

B. In complete sentences, use a specific example to justify your equation from part A. Include a drawing in your answer.

(the picture is for question number two)

1. m(x) = 1.5x

2. -4

3. a) p = 4x  , b) In explanation

Step-by-step explanation:

1. If you look at what the relationship is between each x value and each m(x) value you can see that you multiply by 1.5 each time. So you take x and multiply it by 1.5 to make m(x) - we can then write this as : x*1.5=m(x) or m(x)=1.5x

2. To find the constant of proportionality you need to think about the equation of the graph being y=mx+c - this graph goes through the origin so c=0 and then to find m we need to look at the slope which can be calculated by looking at the change in y divided by the change in x. For every increase of one in the x direction the graph decreases by 4 in the y direction.

So the change in y = -4 (a decrease of 4)

the change in x = 1

-4/1 = -4

3. To find the perimeter you add up all the sides.  In a square all the sides are the same length (we can call this length x) - the perimeter would then be p = x+x+x+x = 4x

this linear equation would have just one solution.

step-by-step explanation:

the reason why this would have one solution is that it is an expression with just one variable. since that variable is not raised to a power, it will always have just one solution.