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Algebra / Linear equations in two variables Difficulty: Easy

What is the equation of the line that passes through the point $left parenthesis 0 comma 5 right parenthesis$ and is parallel to the graph of $y = 7 x + 4$ in the xy-plane?

$y equals 5 x$

$y = 7 x + 5$

$y equals 7 x$

$y = 5 x + 7$

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Explanation

Choice B is correct. The equation of a line in the xy-plane can be written in slope-intercept form $y = m x + b$ , where $m$ is the slope of the line and $left parenthesis 0 comma b right parenthesis$ is its y-intercept. It’s given that the line passes through the point $left parenthesis 0 comma 5 right parenthesis$ . Therefore, $b equals 5$ . It’s also given that the line is parallel to the graph of $y = 7 x + 4$ , which means the line has the same slope as the graph of $y = 7 x + 4$ . The slope of the graph of $y = 7 x + 4$ is $7$ . Therefore, $m equals 7$ . Substituting $7$ for $m$ and $5$ for $b$ in the equation $y = m x + b$ yields $y = 7 x + 5$ .

Choice A is incorrect. The graph of this equation passes through the point $left parenthesis 0 comma 0 right parenthesis$ , not $left parenthesis 0 comma 5 right parenthesis$ , and has a slope of $5$ , not $7$ .

Choice C is incorrect. The graph of this equation passes through the point $left parenthesis 0 comma 0 right parenthesis$ , not $left parenthesis 0 comma 5 right parenthesis$ .

Choice D is incorrect. The graph of this equation passes through the point $left parenthesis 0 comma 7 right parenthesis$ , not $left parenthesis 0 comma 5 right parenthesis$ , and has a slope of $5$ , not $7$ .