If $m=5$, and $(x, y)=(-3,-8)$, solve $y=m x+b$ for $b$.
Answer (1)
Substitute the given values m = 5 and ( x , y ) = ( − 3 , − 8 ) into the equation y = m x + b .
Simplify the equation to − 8 = − 15 + b .
Add 15 to both sides to isolate b : − 8 + 15 = b .
Determine the value of b : b = 7 .
Explanation
Understanding the Problem We are given the equation y = m x + b , and we want to find the value of b when m = 5 and ( x , y ) = ( − 3 , − 8 ) .
Substituting the Values Substitute the given values into the equation: y = m x + b becomes − 8 = 5 ( − 3 ) + b .
Simplifying Simplify the equation: − 8 = − 15 + b .
Solving for b To solve for b , add 15 to both sides of the equation: − 8 + 15 = − 15 + b + 15 , which simplifies to 7 = b .
Final Answer Therefore, the value of b is 7.
Examples
Imagine you're determining the fixed cost of a service. You know the total cost ( y ) depends on a per-unit charge ( m ) and the number of units used ( x ), plus a fixed cost ( b ). If the total cost is -8 when you use -3 units at a per-unit charge of 5, this problem helps you calculate that fixed cost. This is useful in budgeting and financial planning to understand the cost structure of various services or products.
