Please answer fully and explain all your steps in a clear and readable paper! a.
ID: 2884318 • Letter: P
Question
Please answer fully and explain all your steps in a clear and readable paper!
a. Read the Summary: Parametric Equations of Line in Section 10.1, page 711. By eliminating the parameter, show that the parametric equations describe a line, and that this line has a slope of b/a. b. Use these equations in part a to write parametric equations for the line through (3, -1) and (1, 4). c. Reverse the orientation and restrict the values of t so that the parametric equations describe a line segment from (3, -1) to (1, 4). d. Write the (rectangular) equation of the line that passes through (3, -1) and (1, 4). Write your final answer in slope-intercept form. Write a set of parametric equations for the line segment using the parameter x = t (the "instant" parametrization). Be sure to give the appropriate restrictions for t. Make sure your line segment has the correct orientation. e. You can also use the parametric equations x = x_0 + (x_1 - x_0)t, y = y_0 + (y_1 - y_0)t on the interval 0 lessthanorequalto t lessthanorequalto 1 to describe a line segment oriented from(x_0, y_0) to (x_1, y_1). Use these to write parametric equations for the line segment from (3, -1) to (1, 4). You don't have to worry about orientation with this set; the correct orientation is built in. f. Parts c, d, and e are three different methods for finding a parametric representation of a line segment. What are some advantages or disadvantages of the methods? Which do you prefer? Why?Explanation / Answer
From the given question,
Let the line passes through (x1,y1) and (x2,y2)
the parametric equation of line is
x= x1 + t(x2-x1)
y=y1+ t(y2-y1)
eliminating t, we get
(x-x1)/(x2-x1)=(y-y1)/(y2-y1)
(y-y1) = [(y2-y1)/(x2-x1)](x-x1)
y= [(y2-y1)/(x2-x1)]x +y1 - [(y2-y1)/(x2-x1)]x1
this is in the form of y= mx + c
slope of line is (y2-y1)/(x2-x1)= b/a
b) line passes through(3,-1) and (1,4)
If line passes through (x1,y1) and (x2,y2)
the parametric equation of line is
x= x1 + t(x2-x1)
y=y1+ t(y2-y1)
x=3 + t(1-3) => x=3-2t
y=-1 +t(4+1) => y=-1 +5t
eliminating t
(x-3)/(-2)=(y+1)/(5)
5x-15=-2y-2
5x+2y=13 (rectangular form)
y= (-5/2) x + (13/2) slope intercept form