Write the rule for this table as an equation. Write your answer as an equation with f first, followed by and equals sign
z=3, f=50
z=4, f=61
z=5, f=72
z=6, f=83
f=11z+17
correct
To find the equation that represents the relationship between z and f in the given table, we need to identify the pattern or rule that connects the values.
By observing the table, we can see that as z increases by 1, f increases by 11. This indicates a linear relationship between z and f.
To write the equation, we use the slope-intercept form: f = mx + b, where m is the slope and b is the y-intercept. In this case, since the table starts at z=3 with f=50, we can determine the equation as follows:
Step 1: Find the slope (m):
The change in f for every increase of 1 in z is 11. Therefore, the slope (m) is 11.
Step 2: Determine the y-intercept (b):
To find the y-intercept, we substitute the values of one set of z and f coordinates into the equation. Using z=3 and f=50:
50 = 11*3 + b
50 = 33 + b
b = 50 - 33
b = 17
Step 3: Write the equation:
With the slope m=11 and the y-intercept b=17, the equation becomes:
f = 11z + 17