Which situation can be represented by the graph of a linear function?
1- The circumference of a circle with respect to radius
2- The height of a person with respect to age
3- The area of a square garden with respect to side length
4- The speed of a car with respect to time
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The correct answer is 1.
You are looking for a relationship between two quantities, that if plotted, would give you a straight line (ie a linear function), so you need to know about the mathematical or logical relationship between the two quantities for each of the possible answers.
For#1, the circumference of a circle is given by the formula 2*pi*r, where r is the radius. So the circumference increases by a constant factor (2*pi) with each change of the radius. This would give you a straight line if you plotted it.
For #2 , we know that generally for a child their height increases with age, but there's no guarentee that the height changes a constant amount with each year. Plus we don't grow anymore after around 18, so the overall trend would not be a straight line if you plotted height vs age. It could look curved or zig-zagged up until 18, then it would flatten out-definitely not a straight line.
For #3, the area of a square is equal to l * l, if l is the side length. This is L^2, or a quadratic. If you plotted this it would look like a curve (1/2 of a parabola actually), so again it's not a straight line.
#4. the speed of a car has nothing to do with time-they're independent so there is no relationship at all. Your speed doesn't necessarily go up or down the longer you're driving. If the question was about the DISTANCE travelled with respect to time at a constant speed that would indeed be a linear function-for each hour travelled at a constant speed, your distance increases by a constant amount. But speed does not depend on time, linearly or otherwise.
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