Line h is defined by 1 5 x + 1 7 y - 70 = 0 . Line j is

Question

Line h is defined by 1 5 x + 1 7 y - 70 = 0 . Line j is perpendicular to line h in the xy -plane. What is the slope of line j ?

Accepted Answer

Choice D is correct. It&rsquo;s given that line h is defined by 1 5 x + 1 7 y - 70 = 0 . This equation can be written in slope-intercept form y = m x + b , where m is the slope of line h and b is the y -coordinate of the y -intercept of line h . Adding 70 to both sides of 1 5 x + 1 7 y - 70 = 0 yields 1 5 x + 1 7 y = 70 . Subtracting 1 5 x from both sides of this equation yields 1 7 y = - 1 5 x + 70 . Multiplying both sides of this equation by 7 yields y = - 7 5 x + 490 . Therefore, the slope of line h is - 7 5 . It&rsquo;s given that line j is perpendicular to line h in the xy -plane. Two lines are perpendicular if their slopes are negative reciprocals, meaning that the slope of the first line is equal to - 1 divided by the slope of the second line. Therefore, the slope of line j is the negative reciprocal of the slope of line h . The negative reciprocal of - 7 5 is - 1 - 7 5 , or 5 7 . Therefore, the slope of line j is 5 7 . Choice A is incorrect. This is the slope of a line in the xy -plane that is parallel, not perpendicular, to line h . Choice B is incorrect. This is the reciprocal, not the negative reciprocal, of - 7 5 . Choice C is incorrect. This is the negative, not the negative reciprocal, of - 7 5 .

Question line-h