The modeled equation for this table is f(x) = 9x + 5.
Creating this model allows you to solve the other parts of your project. In order to find this equation, you need to start by finding the slope. Slope (m) can be found by using two points in the slope equation listed below.
m = (y1 - y2)/(x1 - x2)
We'll use the first two points for this equation.
m = (23 - 14)(2 - 1)
m = 9/1
m = 9
Now that we have slope, we can plug into the slope intercept form (y = mx + b) along with any ordered pair to find the y-intercept (b)
y = mx + b
14 = 9(1) + b
14 = 9 + b
5 = b
So knowing those two things allows us to write an equation as y = 9x + 5.
If you use this equation, you'll be able to graph like they ask in part 2. The process we followed is step 3. The equation is step 4. That leaves us with just finding what the 10th week will give. Since x stands for weeks, we can just use x = 10 to find f(x).
f(x) = 9x + 5
f(x) = 9(10) + 5
f(x) = 90 + 5
f(x) = 95
