Question

Rewrite the parametric equations by eliminating the parameter:

x = 2t + 3 and y equals t minus 2.
(1 point)
Responses

y = 3x + 1
y = 3 x + 1

y equals Start Fraction x minus 7 over 2 End Fraction
Image with alt text: y equals Start Fraction x minus 7 over 2 End Fraction

y = x + 5
y = x + 5

y equals Start Fraction x minus 5 over 2 End Fraction

Answer 1

To eliminate the parameter \( t \) from the given parametric equations \( x = 2t + 3 \) and \( y = t - 2 \), we can solve for \( t \) in terms of \( x \):

1. From the equation \( x = 2t + 3 \), we can isolate \( t \):
\[
2t = x - 3
\]
\[
t = \frac{x - 3}{2}
\]

2. Next, substitute this expression for \( t \) into the equation for \( y \):
\[
y = t - 2 = \frac{x - 3}{2} - 2
\]
\[
y = \frac{x - 3}{2} - \frac{4}{2} = \frac{x - 3 - 4}{2} = \frac{x - 7}{2}
\]

Thus, the relation between \( x \) and \( y \) is given by:
\[
y = \frac{x - 7}{2}
\]

This means the correct response is:
**y equals Start Fraction x minus 7 over 2 End Fraction**