If $x=8$ for the equation $y=\frac{1}{2} x-3$, what is $y$?
Answer (2)
Substitute x = 8 into the equation y = 2 1 x − 3 .
Calculate 2 1 × 8 = 4 .
Subtract 3 from the result: 4 − 3 = 1 .
The value of y is 1 .
Explanation
Understanding the Problem We are given the equation y = 2 1 x − 3 and we are asked to find the value of y when x = 8 . This is a straightforward substitution problem.
Substituting the Value of x To find the value of y , we substitute x = 8 into the equation: y = 2 1 ( 8 ) − 3
Simplifying the Expression Now, we simplify the expression: y = 4 − 3
Calculating the Value of y Finally, we perform the subtraction: y = 1
Stating the Final Answer Therefore, when x = 8 , the value of y is 1.
Examples
Imagine you're baking a cake and the recipe says you need half the amount of sugar as flour, minus 3 tablespoons. If you use 8 tablespoons of flour, this problem shows you how to calculate the exact amount of sugar needed to follow the recipe correctly. This kind of calculation is useful in many real-life situations, from cooking and construction to financial planning, where understanding linear relationships helps in making accurate adjustments and predictions.
Substituting x = 8 into the equation y = \frac{1}{2}x - 3 results in y = 1 after performing the operations. First, we calculate \frac{1}{2}(8) which gives 4, and then subtract 3 to find y = 1. Thus, the value of y when x equals 8 is 1.
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