This quiz covers linear equations.  Please do your work on clean paper, and then upload your work to your instructor.  Show any intermediate steps in addition to the final answer(s).  You may use any of your notes from the quarter, as well as any resources on the Canvas site and Desmos if you desire.

1.  A beading pattern consists of a central triangle, three arms that go outwards, and a triangle at the end of each arm.  Sketches of pattern for size 1 and size 3 are shown below.  If each triangle requires 6 beads and each square requires 9 beads, how many beads are required for a pattern of size 5?  How many beads are required for a pattern of any size x?

Size 1                                                                                           Size 3

1.  Create a small table that shows the number of beads for at least sizes 1, 2, and 3.
2. Describe in words how you see the pattern growing.
3. Determine a formula for the number of beads.  Use x for size and y for the number of beads.
4. Graph your formula.
•  Graph the line Y = -3X + 4.  Clearly describe how you determined the graph, even if you use Desmos to make the picture.
• Consider the two linear expressions A and B.  For what value of X are the two expressions equal?  See complete questions on next page.

A:  2X + 3

B:  10 – 3X

1. Draw a picture of the equation (balance beam).
2. Try several values for x and record tilt.  Include at least one value which causes L tilt and at least one value causing R tilt.
3. Algebraically solve for the balance point (equality).
4. Indicate the range of values for which expression A is LESS THAN expression B.
5. Provide a graph of the two lines indicating the balance point.
•  What is the equation of the line shown on the graph below?  What is the slope and what is the y-intercept?

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