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Chapter 3: Q1P (page 112)

In Problems 1 to 5, all lines are in the (x,y) plane.

  1. Write the equation of the straight line through(2,-3) with slope 3/4, in the parametric formr=r0+At.

Short Answer

Expert verified

The parametric equation of the line is (2,-3)+(4,3)t.

Step by step solution

01

Concept of the straight line in slope form.

Write the expression of the straight line in slope form.

y-yox-xo=m......(1)

Here, is the slope and and are the coordinates.

02

Find the equation of the Straight line

The given point is (2,-3) and the slope of line is 34.

Substitute -3 foryo,2forxoand34formin equation (1).

y-(-3)x-(2)=34y+33=x-24

Thus, from the obtained equation, a=4 and b=3 in parametric form.

03

Substitute the value in parametric form

The parametric form is,x=2+4t.

And,y=-3+3t.

Thus, the parametric equation can be written as follows:

r=(2,-3)+(4,3)t

Therefore, the parametric equation of the line is (2,-3)+(4,3)t.

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Most popular questions from this chapter

Let each of the following matrices M describe a deformation of the(x,y)plane For each given M find: the Eigen values and eigenvectors of the transformation, the matrix Cwhich Diagonalizes Mand specifies the rotation to new axes(x',y')along the eigenvectors, and the matrix D which gives the deformation relative to the new axes. Describe the deformation relative to the new axes.

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