How do you write an equation for the linear function shown in the table?
X f(x)
-3 8
3 4
6 2
9 0
Please help and explain how to do this. Thank you :)
To write an equation for a linear function, we need to find the slope (m) and the y-intercept (b). The slope represents the rate of change, and the y-intercept represents the value of f(x) when x is zero.
To find the slope, we can use the formula:
m = (change in f(x)) / (change in x)
Let's find the change in f(x) and change in x for two points on the table:
For the points (-3, 8) and (6, 2):
Change in f(x) = 2 - 8 = -6
Change in x = 6 - (-3) = 9
Therefore, the slope is:
m = -6 / 9 = -2/3
Next, to find the y-intercept, we can substitute one of the points into the equation y = mx + b and solve for b.
Using the point (3, 4):
4 = (-2/3)(3) + b
Simplifying this equation, we get:
4 = -2 + b
b = 4 + 2 = 6
Therefore, the equation for the linear function is:
y = (-2/3)x + 6
In the equation y = (-2/3)x + 6, x represents the input value, and y represents the output value or the value of f(x).
So, to evaluate the function for any x-value, substitute that value into the equation and solve for y.