Question

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 :

Answer 1

No, yes, yes

(-28,-11) and (8.7)

`[tex][(-4)/(3) ,\infty)`}[/tex]

Explanation:

Given that a line in two dimension is parametrized by

`x=2+6t \\y = 4+3t`

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 = 4

b) when t lies between -2 and 1

we have left end point as

`x=2+6(-2) = -10\\y = 4+3(-2) = -2\\`

(-10,-2) is left end point

Right end point is when t =1 i.e.

(8,7)

c) when the points should be above x axis, y should be non negative

i.e.
`y=4+3t\geq 0\\t\geq`

So t should lie in the interval

`[(-4)/(3) ,\infty)`}