Graph the parametric equation x = 2t y = t + 5, -2 ≤ t ≤ 3

Accepted Solution

Just fun I'm going to add something above the below.You can write an equation for this without the parameter.You have y=t+5 and x=2t.  If you multiply both sides of y=t+5 by 2 you should get 2y=2t+10 and guess what you can replace 2t with x since you have x=2t.  So you can write 2y=x+10 as your equation to represent the parametric version they have here.This is a linear equation as our graph appears to be below.   Solve for y by dividing both sides by 2 gives you y=x/2  +5.  The slope is 1/2 and the y-intercept is 5.  If t is between -2 and 3 then x is between -4 and 6 since x is doubled t (inclusive here since we have those equal signs along with those inequalities). So you could have just graph the line y=x/2+5 on the interval [tex]-4 \le x \le 6 [/tex]/Anyways, I'm also going to look at this without the rewrite: I'm going to make a table with 4 columns.  The first column is t.  The second is x(t), the third is y(t), and the fourth will be a list of points (x,y) our relation will go through). t    |     x(t)        |     y(t)           |   (x,y)-------------------------------------------------------2       2(-2)=-4      -2+5=3          (-4,3)-1        2(-1)=-2       -1+5=4           (-2,4)0        2(0)=0         0+5=5           (0,5)1         2(1)=2           1+5=6           (2,6)2        2(2)=4          2+5=7          (4,7)3        2(3)=6          3+5=8           (6,8)Now I'm going to graph the points in the last column on a coordinate-plane.The horizontal axis is your x-axis and the vertical axis is your y-axis. I did the x-axis going up or down by two's while the y-axis is going up and down only by one's.