A line is parameterized by x=2+6???? and y=4+3????. (a) Which of the following points are on the section of the line obtained by restricting ???? to nonnegative numbers (for each, enter Y if the point is on the section, and N if not)? (−28,−11) : (8,7) : (26,16) : Then, give one more point that is on the section of the line obtained by this restriction: (b) What are the endpoints of the line segment obtained by restricting ???? to −2≤????≤1? left endpoint : right endpoint : (c) How should ???? be restricted to give the part of the line above the x-axis (give your answer as an interval for ????, for example, (3,8) or [-2,Inf))? ???? must be in :

Accepted Solution

Answer:No, yes, yes(-28,-11) and (8.7)[tex][tex][\frac{-4}{3} ,\infty)[/tex]}[/tex]Step-by-step explanation:Given that a line in two dimension is parametrized by[tex]x=2+6t \\y = 4+3t[/tex]a) If t is non negative, then (-28,-11) cannot lie on that part(-28,-11) No because t =-5(8,7) yes because t =1(26,16) yes because t = 4b) when t lies between -2 and 1we have left end point as [tex]x=2+6(-2) = -10\\y = 4+3(-2) = -2\\[/tex](-10,-2) is left end pointRight end point is when t =1 i.e. (8,7)c) when the points should be above x axis, y should be non negativei.e. [tex]y=4+3t\geq 0\\t\geq [/tex]So t should lie in the interval[tex][\frac{-4}{3} ,\infty)[/tex]}