create a graph using the parametric curve.

x=t-1
y=2t+4
-3 is less than or equal to t, is less than or equal to 2

Here is the graph of the parametric curve defined by the equations \(x = t - 1\) and \(y = 2t + 4\), for \( t \in [-3, 2] \).

Would you like further details about the graph or the curve? Feel free to ask if you have any questions!

Here are some related questions:
1. How would the graph change if the equation for \(y\) was altered to \(y = 3t + 4\)?
2. Can you describe how the slope of the curve is determined from the parametric equations?
3. What is the significance of the domain of \(t\) in the parametric equations?
4. How do you convert this parametric form into a single Cartesian equation?
5. What would happen if you extended the domain of \(t\) beyond the given range?

**Tip:** In parametric equations, each parameter (in this case, \(t\)) controls both the \(x\) and \(y\) values, offering flexibility to describe curves that are not functions in the standard \(y = f(x)\) sense.

Create a graph using the parametric curve: x = t - 1, y = 2t + 4, for -3 ≤ t ≤ 2

Learn how to graph a parametric curve defined by x = t - 1 and y = 2t + 4, with the parameter t in the range [-3, 2]. This lesson explains how to use parametric equations to plot points and understand the resulting graph. Ideal for high school students in Grades 10-12.

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