Find the slope of the line whose parametric equations are x=4t+6 and y=t-1

Options

A. -4
B. 44200
C. 4
D. `1/4`

Answer

To find the slope of the line defined by the parametric equations \( x = 4t + 6 \) and \( y = t - 1 \), we will follow these steps:

### Step 1: Differentiate the Parametric Equations
We start by differentiating both \( x \) and \( y \) with respect to the parameter \( t \).

1. Differentiate \( x \):
\[ \frac{dx}{dt} = \frac{d}{dt}(4t + 6) = 4 \]

2. Differentiate \( y \):
\[ \frac{dy}{dt} = \frac{d}{dt}(t - 1) = 1 \]

### Step 2: Find the Slope \( \frac{dy}{dx} \)
The slope of the line can be found using the formula for the derivative of \( y \) with respect to \( x \):
\[ \frac{dy}{dx} = \frac{dy/dt}{dx/dt} \]
Substituting the derivatives we found in Step 1:
\[ \frac{dy}{dx} = \frac{1}{4} \]

### Conclusion
Thus, the slope of the line whose parametric equations are given is:
\[ \frac{1}{4} \]

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