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Algebra / Linear functions Difficulty: Medium

Distance (kilometers)	Average time (minutes)
$0.32$ $0.32$	$8$ $8$
$0.56$ $0.56$	$14$ $14$
$0.68$ $0.68$	$17$ $17$

The table gives the average time $t$ $t$ , in minutes, it takes Carly to travel a certain distance $d$ $d$ , in kilometers. Which equation could represent this linear relationship?

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Explanation

Choice C is correct. The average time $t$ $t$ , in minutes, it takes Carly to travel a certain distance $d$ $d$ , in kilometers, is given in the table. This linear relationship can be represented by an equation in the form $t = a d + b$ $t = a d + b$ , where $a$ $a$ and $b$ $b$ are constants. The table shows that it takes Carly an average time of $8$ $8$ minutes to travel $0.32$ $0.32$ kilometers. Substituting $8$ $8$ for $t$ $t$ and $0.32$ $0.32$ for $d$ $d$ in the equation $t = a d + b$ yields $8 = 0.32 a + b$ . Subtracting $0.32 a$ from both sides of this equation yields $8 - 0.32 a = b$ . The table also shows that it takes Carly an average time of $14$ minutes to travel $0.56$ kilometers. Substituting $14$ for $t$ and $0.56$ for $d$ in the equation $t = a d + b$ yields $14 = 0.56 a + b$ . Subtracting $0.56 a$ from both sides of this equation yields $14 - 0.56 a = b$ . Substituting $8 minus 0.32 a$ for $b$ in this equation yields $14 - 0.56 a = 8 - 0.32 a$ . Subtracting $8$ from both sides of this equation yields $6 - 0.56 a = - 0.32 a$ . Adding $0.56 a$ to both sides of this equation yields $6 equals 0.24 a$ . Dividing both sides of this equation by $0.24$ yields $25 equals a$ . Substituting $25$ for $a$ in the equation $8 = 0.32 a + b$ yields $8 = 0.32 (25) + b$ , or $8 = 8 + b$ . Subtracting $8$ from both sides of this equation yields $0 equals b$ . Substituting $25$ for $a$ and $0$ for $b$ in the equation $t = a d + b$ yields $t = 25 d + 0$ , or $t equals 25 d$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.