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Algebra / Linear equations in two variables Difficulty: Easy

$x$ $x$	$y$ $y$
$0$ $0$	$18$ $18$
$1$ $1$	$13$ $13$
$2$ $2$	$8$ $8$

The table shows three values of $x$ and their corresponding values of $y$ . There is a linear relationship between $x$ and $y$ . Which of the following equations represents this relationship?

$y = 18 x + 13$

$y = 18 x + 18$

$y = - 5 x + 13$

$y = - 5 x + 18$

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Explanation

Choice D is correct. A linear relationship can be represented by an equation of the form $y = m x + b$ , where $m$ and $b$ are constants. It’s given in the table that when $x equals 0$ , $y equals 18$ . Substituting $0$ for $x$ and $18$ for $y$ in $y = m x + b$ yields $18 = m (0) + b$ , or $18 equals b$ . Substituting $18$ for $b$ in the equation $y = m x + b$ yields $y = m x + 18$ . It’s also given in the table that when $x equals 1$ , $y equals 13$ . Substituting $1$ for $x$ and $13$ for $y$ in the equation $y = m x + 18$ yields $13 = m (1) + 18$ , or $13 = m + 18$ . Subtracting $18$ from both sides of this equation yields $- 5 = m$ . Therefore, the equation $y = - 5 x + 18$ represents the relationship between $x$ and $y$ .

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 C is incorrect and may result from conceptual or calculation errors.