Parametric equation true/false

[-EquinoX-]

Homework Statement

(a) The parametric curve x = (3t + 4)2, y = (3t + 4)2 - 9 for 0 t 3 is a line segment.
(b) A parameterization of the graph of y = lnx for x > 0 is given by x = et, y = t for - < t < .
(c) The line parameterized by x = 8, y = 5t, z = 6 + t is parallel to the x-axis.

Homework Equations

The Attempt at a Solution

a. false
b. true
c. true

Is my answer correct? If its false can someone help me to explain why

 

[alligatorman]

You should provide the reasoning behind your answers.

 

[-EquinoX-]

for part a, it's just a mere guess as I see a ^2 there, so I thought it wouldn't be a line
for part b I think because when you plugged in the graph you get the same
for part c, the two lines aren't multiples of each other... 5j + k and 1i

 

[Rachel74510]

was your answer correct?

 

[Char. Limit]

For equation 1, try finding an equation for y in terms of x. It should be pretty easy. Then you'll easily see whether it's a line or not.

 

[HallsofIvy]

for part a, it's just a mere guess as I see a ^2 there, so I thought it wouldn't be a line

Actually, the way you wrote it, there is NO "^2".
A way of seeing that it is not a line is to choose three values of t giving three points on the graph. Find the slopes between two pairs of points. If they are not the same, it is not a line.

for part b I think because when you plugged in the graph you get the same

That sentence doesn't make sense to me. How do "plug in" a graph? And what does "the same" refer to?

for part c, the two lines aren't multiples of each other... 5j + k and 1i

Because the "two lines aren't multiples of each other", you say the line is parallel to the x-axis?