Explain how to write a function rule from the table below. Then write a function rule.
X -2, -1, 0, 1, 2,
Y 2.8, 3.4, 4, 4.6, 5.2
Please help
since the y values differ by 0.6, and y(0)=4
y = 0.6x + 4
To write a function rule from a table, we want to find the relationship between the inputs (X-values) and outputs (Y-values).
Looking at the X-values, we can see that they increase by 1 each time. Similarly, the Y-values also increase by a consistent amount, which in this case is 0.6.
To write the function rule, we can use the formula:
Y = mx + b
Where 'm' represents the slope or rate of change, and 'b' represents the y-intercept.
To find the slope, we can choose any two points from the table and use the formula:
m = (Y₂ - Y₁) / (X₂ - X₁)
Let's use the first two points (-2, 2.8) and (-1, 3.4):
m = (3.4 - 2.8) / (-1 - (-2))
m = 0.6 / 1
m = 0.6
Now that we have the slope, we can substitute it into the function rule and choose any point from the table to find the y-intercept, 'b'. Let's use the first point (-2, 2.8):
2.8 = 0.6 * (-2) + b
2.8 = -1.2 + b
b = 2.8 + 1.2
b = 4
Therefore, the function rule for the table is:
Y = 0.6X + 4