💡 #6.
The table represents some points on the graph of a linear function. Write a function that represents this relationship.
table-
-7.5 12
-3.5 0
-1 -7.5
2 -16.5
3.5 -21
To find the linear function that represents this relationship, we first need to find the slope (m) of the line using two points from the table. Let's use (-7.5, 12) and (3.5, -21).
m = (y2 - y1) / (x2 - x1)
m = (-21 - 12) / (3.5 + 7.5)
m = -33 / 11
m = -3
Now that we have the slope, we can use the point-slope form of a linear equation to find the function:
y - y1 = m(x - x1)
Let's choose the point (3.5, -21) to substitute:
y - (-21) = -3(x - 3.5)
y + 21 = -3x + 10.5
y = -3x + 10.5 - 21
y = -3x - 10.5
Therefore, the linear function that represents the relationship is:
f(x) = -3x - 10.5