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Algebra / Linear equations in two variables Difficulty: Medium

Line $r$ $r$ is defined by the equation $4 x - 9 y = 3$ $4 x - 9 y = 3$ . Line $s$ $s$ is parallel to line $r$ $r$ in the xy-plane. What is the slope of line $s$ $s$ ?

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Explanation

Choice B is correct. It's given that line $s$ $s$ is parallel to line $r$ $r$ in the xy-plane. This means that the slope of line $r$ $r$ is equal to the slope of line $s$ $s$ . Line $r$ $r$ is defined by the equation $4 x - 9 y = 3$ $4 x - 9 y = 3$ . This equation can be written in slope-intercept form $y = m x + b$ $y = m x + b$ , where $m$ $m$ represents the slope of the line and $b$ $b$ represents the y-coordinate of the y-intercept of the line. Subtracting $4 x$ $4 x$ from both sides of the equation $4 x - 9 y = 3$ $4 x - 9 y = 3$ yields $- 9 y = - 4 x + 3$ $- 9 y = - 4 x + 3$ . Dividing both sides of this equation by $- 9$ $negative 9$ yields $y = \frac{4}{9} x - \frac{1}{3}$ $y = \frac{4}{9} x - \frac{1}{3}$ . Therefore, the slope of line $r$ $r$ is $\frac{4}{9}$ $\frac{4}{9}$ . Since parallel lines have equal slopes, the slope of line $s$ $s$ is also $\frac{4}{9}$ $\frac{4}{9}$ .

Choice A is incorrect. This is the reciprocal of the slope of line $s$ $s$ , not the slope of line $s$ $s$ .

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

Choice D is incorrect and may result from conceptual or calculation errors.