To find the output for the rule "seven increased by five times a number," you can express it mathematically as:
\[ 7 + 5x \]
where \( x \) is the number you're providing as input. In this case, \( x = -2 \).
Now, substitute \(-2\) for \(x\):
\[ 7 + 5(-2) \]
Calculate the multiplication first:
\[ 5(-2) = -10 \]
Now, substitute that back into the equation:
\[ 7 - 10 \]
Finally, calculate the result:
\[ 7 - 10 = -3 \]
So the output for the given rule and input is \(-3\).