Find the cartesian equation of the curve whose parametric equations are :
`x=t, y=3t+5`

Answer

To find the Cartesian equation of the curve given the parametric equations \( x = t \) and \( y = 3t + 5 \), we will follow these steps:

### Step 1: Identify the parametric equations
We have:
- \( x = t \)
- \( y = 3t + 5 \)

### Step 2: Solve for \( t \) in terms of \( x \)
From the first equation, we can express \( t \) as:
\[ t = x \]

### Step 3: Substitute \( t \) in the equation for \( y \)
Now, we substitute \( t \) in the equation for \( y \):
\[ y = 3t + 5 \]
Replacing \( t \) with \( x \):
\[ y = 3x + 5 \]

### Step 4: Write the Cartesian equation
The Cartesian equation of the curve is:
\[ y = 3x + 5 \]

### Conclusion
Thus, the Cartesian equation of the curve is \( y = 3x + 5 \).

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