Write the rule for each function. Write the rule as an equation.
Input x 1 2 3 4 5 6
Output y 6 7 8 9 10 11
Rule: _________________________________________________.
Input x 1 2 3 4 5 6
Output y 5 8 11 14 17 20
Rule: _________________________________________________.
Input x 1 2 3 4 5 6
Output y 4.5 5 5.5 6 6.5 7
Rule: _________________________________________________.
Input h 1 2 3 4 5 6
Output w 4 7 10 13 16 19
Rule: _________________________________________________.
these are all linear functions, since the output changes by a fixed amount when the input does.
The ratio of the changes is the slope of the line.
For example, the last one has a slope of 3, since when x increases by 1, y increases by 3 every time. So, you want a rule that looks like
y = 3x
However, when x=1, 3x=3, but y=4. So, adjust it by 1, and you have the rule
y = 3x+1
which you can see fits the table.
Work the others the same way.
Rule: y = x + 5
Rule: y = 3x + 2
Rule: y = 0.5x + 4
Rule: w = 3h + 1
Rule for the first function:
y = x + 5
Rule for the second function:
y = 3x + 2
Rule for the third function:
y = 0.5x + 4
Rule for the fourth function:
w = 3h + 1
To write the rule for each function as an equation, we need to identify the pattern between the input (x or h) and the output (y or w) values.
For the first function:
Input x 1 2 3 4 5 6
Output y 6 7 8 9 10 11
From the given values, we can see that for each input x, the output y is obtained by adding 5 to x. So, the rule for this function can be written as:
y = x + 5
For the second function:
Input x 1 2 3 4 5 6
Output y 5 8 11 14 17 20
From the given values, we can see that for each input x, the output y is obtained by multiplying x by 3 and then subtracting 1. So, the rule for this function can be written as:
y = 3x - 1
For the third function:
Input x 1 2 3 4 5 6
Output y 4.5 5 5.5 6 6.5 7
From the given values, we can see that for each input x, the output y is obtained by adding 0.5 to x. So, the rule for this function can be written as:
y = x + 0.5
For the fourth function:
Input h 1 2 3 4 5 6
Output w 4 7 10 13 16 19
From the given values, we can see that for each input h, the output w is obtained by multiplying h by 3 and then adding 1. So, the rule for this function can be written as:
w = 3h + 1