Give parametric equations that generate the line with slope -2 passing through (1, 3).

Question

Poul1963 · Accepted Answer

Step 1
Concept:
The calculus helps in understanding the changes between values that are related by a function. It is used in different areas such as physics, biology and sociology and so on. The calculus is the language of engineers, scientists and economics.
Step 2
Given:
Slope

= - 2

The given point is (1,3)
The objective is to give the parametric equation that generate the line with the given slope and the point
Step 3
It is known that the line passing through the point

(x_{0}, y_{0})

and having the slope

\frac{b}{a}

then the parametric equations of such a line are as follows

x = x_{0} + a t, y = y_{0} + b t, - \infty < t < \infty (x_{0}, y_{0}) = (1, 3)

Since slope

\frac{b}{a} = - \frac{2}{1}

Hence

x = 1 + t, y = 3 - 2 t, - \infty < t < \infty

Step 4

(x_{0}, y_{0}) = (1, 3)

Since slope

\frac{b}{a} = - \frac{2}{1}

Hence

x = 1 + t, y = 3 - 2 t, - \infty < t < \infty

are the parametric equations of the required line

Give parametric equations that generate the line with slope -2

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