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Problem 9

This function is linear because each time x goes up by 1, y goes up by 3. This represents a slope of rise/run = 3/1 = 3. The slope is the rate of change.

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Problem 10

We have y decreasing at first (y = 4 to y = 1 to y = 0), but then y increases after y = 0. This is sufficient info to prove the function isn't linear. A linear function either always increases, always decreases, or is constant (aka a flat horizontal line).

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The graph on the left has us start with (0,4) as the y intercept, due to b = 4. We then drop down 2, and move to the right 3 to get to the next point (3,2). The "down 2, right 3" motion is directly because of the slope m = -2/3.

The graph of the right has the points (-2,0) and (0,3) as the x and y intercepts in that order. This is from a = -2 and b = 3 given by your teacher. We only need 2 points to form a straight line.