help me learn this question---Question Stem:
Given that y = 112 when x = 4, work out the value of k.
Other Relevant Text:
Give any decimal answers to 1 d.p.
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We have a problem where y equals 112 when x equals 4, and we need to find the value of k. We assume this follows a direct variation relationship, where y equals k times x. Let's visualize this with the given point on a coordinate system.
Now we substitute the given values into our formula. We know that y equals 112 and x equals 4. Substituting these into y equals k times x gives us 112 equals k times 4. This creates an equation we can solve for k.
Now we solve for k by dividing both sides of the equation by 4. We have 112 equals k times 4. Dividing both sides by 4 gives us 112 divided by 4 equals k. Calculating 112 divided by 4 gives us 28. Therefore, k equals 28.
Let's verify our answer by substituting k equals 28 back into the original equation. When k equals 28 and x equals 4, we get y equals 28 times 4, which equals 112. This matches our given value, confirming our answer is correct. Therefore, k equals 28, which is already expressed to 1 decimal place.
To summarize what we learned: We identified this as a direct variation problem where y equals k times x. We substituted the given values and solved the resulting equation to find that k equals 28. Finally, we verified our answer by checking it against the original condition.