Answers are
a) is a function y = -1/3x + 5
b. Is NOT a function, the slope / rate changes so it won’t be a straight line
Step by step
a. Rate is proportional -1/3 slope so it is a function
To write a linear function, you need the slope and the y-intercept.
We will use slope formula for two pairs to find slope
y2-y1 over x2-x1
(-2, 5 2/3) and (0, 5)
5 - 5 2/3 over 0 - -2
-2/3 over 2
Divide
-2/3 * 1/2 = -1/3
(2, 4 1/3) and (4, 3 2/3)
3 2/3 - 4 1/3 over 4 - 2
-2/3 over 2
Divide
-2/3 * 1/2 = -1/3
We found slope is -1/3
Now we can find our equation by using point slope form and points (0, 5)
y - 5 = -1/3 (x - 0)
y -5 = -1/3x
add 5 to both sides to solve for y
y -5 +5 = -1/3x + 5
Combine
y = -1/3x + 5 your answer
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b. Reason, use slope formula for two pairs
y2-y1 over x2-x1
(-5, -27) and (0, -2)
-2 - -27 over 0 - -5
25 over 5, slope is 5
(5, 20) and (10, 48)
48 - 20 over 10 - 5
28 over 5, slope is 5 3/5
Slope of 5 and slope of 5 3/5 are not the same so the line will not be a straight line and it won’t be a linear function