How do I do this, some plz help:
"Eliminate the parameter t and identify the graph of the parametric equations.
Given: x = 3t-2, y=t + 1, -∞ < t < ∞"
solve each for t
x = 3t-2 ----> t = (x+2)/3
y = t+1 -----> t = y-1
now equate (x+2)/3 to y-1 and simplify
You should be able to identify that function and its graph
Thank you for replying, but how do u equate (x+2)/3 to y-1
If t = (x+2)/3 and
t = y-1
the two "right sides" are equal to the same thing, so they are equal to each other.
(if Sam weighs 65 kg, and Bill weighs 65 kg, then Sam weighs the same as Bill)
To eliminate the parameter, t, and identify the graph of the parametric equations x = 3t - 2 and y = t + 1, you need to find an equation that describes the relationship between x and y.
To eliminate t, you can solve one of the equations for t and substitute it into the other equation. Let's solve the first equation, x = 3t - 2, for t:
x = 3t - 2
x + 2 = 3t
t = (x + 2)/3
Now substitute this expression for t into the second equation, y = t + 1:
y = (x + 2)/3 + 1
y = (x + 2)/3 + 3/3
y = (x + 5)/3
So the equation that describes the relationship between x and y is y = (x + 5)/3. This is the equation of the graph.
Now, let's analyze the graph. The equation y = (x + 5)/3 represents a straight line with a slope of 1/3 and a y-intercept of 5/3. The line will extend infinitely in both directions since the parameter t ranges from -∞ to ∞.
Therefore, the graph of the parametric equations x = 3t - 2 and y = t + 1 is a straight line with a slope of 1/3 and a y-intercept of 5/3.