Proportionality>Identifying Examples of Proportional and Non-Proportional Functions(TEKS.Math.8.5.H)
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Texas 8th Grade Math › Proportionality>Identifying Examples of Proportional and Non-Proportional Functions(TEKS.Math.8.5.H)
Which situation represents a proportional function?
The cost of apples is a constant price per pound with no bag or checkout fee.
A gym charges a monthly membership fee plus a fee each time you attend a class.
A taxi fare includes a base fee plus a charge for each mile.
The area of a square depends on the length of its side.
Explanation
Proportional relationships have the form $y=kx$ and pass through the origin. Paying a constant price per pound has no starting fee, so cost is directly proportional to weight. The gym and taxi include fixed fees (non-proportional linear, $y=mx+b$ with $b\ne0$). Area of a square varies as $s^2$ (nonlinear).
A ride-share service charges 1.50 dollars per mile plus a base fee of 3 dollars. Identify the type of function relating total cost to miles traveled.
Proportional function ($y=kx$)
Nonlinear relationship
Non-proportional linear function ($y=mx+b$, $b\ne 0$)
Quadratic function with vertex at the origin
Explanation
The cost has a constant rate per mile (slope $m=1.5$) and a fixed starting fee ($b=3$), so it is linear with nonzero intercept: $y=1.5x+3$. That is non-proportional linear ($y=mx+b$ with $b\ne0$), not proportional ($y=kx$).
Which situation is a non-proportional linear relationship?
Distance traveled at a constant speed starting from 0 miles.
The price of bagels is 6 dollars per dozen with no additional fee.
The area of a square as a function of its side length.
A parking garage charges 5 dollars to enter plus 2 dollars per hour.
Explanation
Non-proportional linear functions have the form $y=mx+b$ with $b\ne0$. The parking cost has a fixed entry fee ($b=5$) and a constant hourly rate ($m=2$). The constant-speed distance and the per-dozen bagel cost both pass through the origin (proportional, $y=kx$). Square area depends on $s^2$ (nonlinear).
A water tank already contains 200 liters of water and is filled at a constant rate of 5 liters per minute. Identify the type of function relating total water to time.
Proportional function ($y=kx$)
Non-proportional linear function ($y=mx+b$, $b\ne 0$)
Exponential function
Inverse variation
Explanation
The situation starts with 200 liters, a nonzero initial value ($b=200$), and adds a constant amount per minute ($m=5$). This is linear with a nonzero intercept: $y=5x+200$, so it is non-proportional linear, not proportional ($y=kx$ passes through the origin).
Which situation represents a proportional relationship?
The mass of apples depends on the number of identical apples chosen.
A streaming plan has a base monthly fee plus a charge per gigabyte used.
Temperature in degrees Fahrenheit as a function of degrees Celsius.
The area of a circle as a function of its radius.
Explanation
With identical apples, total mass scales directly with the number of apples and starts at 0, so $y=kx$ (proportional). A streaming plan with a base fee is non-proportional linear ($y=mx+b$, $b\ne0$). Fahrenheit vs. Celsius is linear with a nonzero intercept ($F=\tfrac{9}{5}C+32$), and circle area is nonlinear ($A=\pi r^2$).