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Algebra / Linear equations in two variables Difficulty: Easy

The graph shows the linear relationship between $x$ and $y$ . Which table gives three values of $x$ and their corresponding values of $y$ for this relationship?

$x$	$y$
$0$	$0$
$1$	$negative 7$
$2$	$negative 9$

$x$	$y$
$0$	$0$
$1$	$negative 3$
$2$	$negative 1$

$x$	$y$
$0$	$negative 5$
$1$	$negative 7$
$2$	$negative 9$

$x$	$y$
$0$	$negative 5$
$1$	$negative 3$
$2$	$negative 1$

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Explanation

Choice D is correct. It’s given that the graph shows the linear relationship between $x$ and $y$ . The given graph passes through the points $left parenthesis 0 comma negative 5 right parenthesis$ , $left parenthesis 1 comma negative 3 right parenthesis$ , and $left parenthesis 2 comma negative 1 right parenthesis$ . It follows that when $x equals 0$ , the corresponding value of $y$ is $negative 5$ , when $x equals 1$ , the corresponding value of $y$ is $negative 3$ , and when $x equals 2$ , the corresponding value of $y$ is $negative 1$ . Of the given choices, only the table in choice D gives these three values of $x$ and their corresponding values of $y$ for the relationship shown in the graph.

Choice A is incorrect. This table represents a relationship between $x$ and $y$ such that the graph passes through the points $left parenthesis 0 comma 0 right parenthesis$ , $left parenthesis 1 comma negative 7 right parenthesis$ , and $left parenthesis 2 comma negative 9 right parenthesis$ .

Choice B is incorrect. This table represents a relationship between $x$ and $y$ such that the graph passes through the points $left parenthesis 0 comma 0 right parenthesis$ , $left parenthesis 1 comma negative 3 right parenthesis$ , and $left parenthesis 2 comma negative 1 right parenthesis$ .

Choice C is incorrect. This table represents a linear relationship between $x$ and $y$ such that the graph passes through the points $left parenthesis 0 comma negative 5 right parenthesis$ , $left parenthesis 1 comma negative 7 right parenthesis$ , and $left parenthesis 2 comma negative 9 right parenthesis$ .