Answer:
y = -3x + 7
Step-by-step explanation:
Using any 2 pairs of values, say (-3, 16) and (-1, 10), therefore, rate of change of the data given = [tex] \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - 16}{-1 -(-3} = \frac{-6}{2} = -3 [/tex].
We would get the same rate of change if we use any other two pairs of values in the data given.
Therefore, the data can be modeled by a linear equation because the rate of change remains constant all through.
To represent y as a function of x, find b, since we know the rate of change (m).
Substitute x = -3, y = 16 and m = -3 in y = mx + b.
Thus:
16 = (-3)(-3) + b
16 = 9 + b
Subtract 9 from each side
16 - 9 = b
7 = b
b = 7
Substitute m = -3 and b = 7 in y = mx + b
The function would be:
✅ y = -3x + 7
