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Algebra / Linear equations in two variables Difficulty: Hard

In the xy-plane, line k is defined by $x plus y equals 0$ . Line j is perpendicular to line k, and the y-intercept of line j is $the point with coordinates 0 comma 3$ . Which of the following is an equation of line j ?

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Explanation

Choice D is correct. It’s given that line j is perpendicular to line k and that line k is defined by the equation $x plus y, equals 0$ . This equation can be rewritten in slope-intercept form, $y equals, m x plus b$ , where m represents the slope of the line and b represents the y-coordinate of the y-intercept of the line, by subtracting x from both sides of the equation, which yields $y equals, negative x$ . Thus, the slope of line k is $negative 1$ . Since line j and line k are perpendicular, their slopes are opposite reciprocals of each other. Thus, the slope of line j is 1. It’s given that the y-intercept of line j is $the point with coordinates 0 comma 3$ . Therefore, the equation for line j in slope-intercept form is $y equals, x plus 3$ , which can be rewritten as $x minus y, equals negative 3$ .

Choices A, B, and C are incorrect and may result from conceptual or calculation errors.