Math Problem Statement

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

Solution

Here is the graph of the parametric curve defined by the equations x=t1x = t - 1 and y=2t+4y = 2t + 4, for t[3,2]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 yy was altered to y=3t+4y = 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 tt 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 tt beyond the given range?

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

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Math Problem Analysis

Mathematical Concepts

Parametric Equations
Graphing
Algebra

Formulas

x = t - 1
y = 2t + 4

Theorems

Graphing Parametric Equations

Suitable Grade Level

Grades 10-12