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Algebra / Linear equations in two variables Difficulty: Easy

$7 x - 4 y = - 84$ $7 x - 4 y = - 84$

For the given equation, which table gives three values of $x$ $x$ and their corresponding values of $y$ $y$ ?

$x$	$0$	$4$	$8$
$y$	$21$	$28$	$35$

$x$	$0$	$4$	$8$
$y$	$35$	$28$	$21$

$x$	$21$	$28$	$35$
$y$	$0$	$4$	$8$

$x$	$21$	$28$	$35$
$y$	$8$	$4$	$0$

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Explanation

Choice A is correct. To verify which table represents this linear relationship, the values in each table can be checked by substituting them into the given equation. The table in choice A shows that when $x = 0$ $x equals 0$ , $y = 21$ $y equals 21$ . Substituting these values into the given equation yields $7 (0) - 4 (21) = - 84$ $7 (0) - 4 (21) = - 84$ , or $- 84 = - 84$ $- 84 = - 84$ , which is true. Additionally, the table in choice A shows that when $x = 4$ $x equals 4$ , $y = 28$ $y equals 28$ . Substituting these values into the given equation yields $7 (4) - 4 (28) = - 84$ $7 (4) - 4 (28) = - 84$ , or $- 84 = - 84$ $- 84 = - 84$ , which is true. Finally, the table in choice A shows that when $x = 8$ $x equals 8$ , $y = 35$ $y equals 35$ . Substituting these values into the given equation yields $7 (8) - 4 (35) = - 84$ $7 (8) - 4 (35) = - 84$ , or $- 84 = - 84$ $- 84 = - 84$ , which is true. Therefore, the table in choice A gives three values of $x$ $x$ and their corresponding values of $y$ $y$ .

Choice B is incorrect. The table in choice B shows that when $x = 0$ $x equals 0$ , $y = 35$ $y equals 35$ . Substituting these values into the given equation yields $7 (0) - 4 (35) = - 84$ $7 (0) - 4 (35) = - 84$ , or $- 140 = - 84$ , which is not true.

Choice C is incorrect. The table in choice C shows that when $x equals 21$ , $y equals 0$ . Substituting these values into the given equation yields $7 (21) - 4 (0) = - 84$ , or $147 = - 84$ , which is not true.

Choice D is incorrect. The table in choice D shows that when $x equals 21$ , $y equals 8$ . Substituting these values into the given equation yields $7 (21) - 4 (8) = - 84$ , or $115 = - 84$ , which is not true.