Line t in the xy -plane has a slope of - 1 3 and passes through the point 9 ,

Question

Line t in the xy -plane has a slope of - 1 3 and passes through the point 9 , 10 . Which equation defines line t ?

Accepted Answer

Choice D is correct. The equation that defines line t in the xy -plane can be written in slope-intercept form y = m x + b , where m is the slope of line t and 0 , b is its y -intercept. It&rsquo;s given that line t has a slope of - 1 3 . Therefore, m = - 1 3 . Substituting - 1 3 for m in the equation y = m x + b yields y = - 1 3 x + b , or y = - x 3 + b . It&rsquo;s also given that line t passes through the point 9 , 10 . Substituting 9 for x and 10 for y in the equation y = - x 3 + b yields 10 = - 9 3 + b , or 10 = - 3 + b . Adding 3 to both sides of this equation yields 13 = b . Substituting 13 for b in the equation y = - x 3 + b yields y = - x 3 + 13 . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect. This equation defines a line that has a slope of 9 , not - 1 3 , and passes through the point 0 , 10 , not 9 , 10 . Choice C is incorrect. This equation defines a line that passes through the point 0 , 10 , not 9 , 10 .

Question 803e7a