Chapter 1.1, Problem 73E

a.

To determine

Calculate the slope − intercept forms of the equations of the lines through the given points which are parallel to the given line.

Answer to Problem 73E

The slope intercept form for the parallel line is $x=3$ .

Explanation of Solution

Given:

It is given in the question that the coordinates and equation are $(3,-2),x-4=0$ .

Concept Used:

In this , use the concept that the slope intercept form is $y=mx+c$ and the parallel line have the same slope.

Calculation: The equation is $x-4=0$ ,make this in slope intercept form,

  $\begin{array}{l}x-4=0\\ x=4\end{array}$

This means there is a vertical line that crosses the point $(4,0)$ .A parallel line has the same slope as the line we are comparing it to.

Remember all vertical lines have an undefined slope.So a line parallel to $x=4$ must also be a vertical line that crosses the point $(3,-2)$ .The only parallel line that fulfills these requirements is $x=3$ .

The parallel line will be : $x=3$ .

Conclusion:

The equation is $x=3$ .

b.

To determine

Calculate the slope − intercept forms of the equations of the lines through the given points which are perpendicular to the given line.

Answer to Problem 73E

The slope intercept form for the perpendicular line is $y=-2$ .

Explanation of Solution

Given:

It is given in the question that the coordinates and equation are $(3,-2),x-4=0$ .

Concept Used:

In this , use the concept that the slope intercept form is $y=mx+c$ and the perpendicular line has a slope that is the negative reciprocal of the line.

Calculation: The equation is $x-4=0$ ,make this in slope intercept form,

  $\begin{array}{l}x-4=0\\ x=4\end{array}$

Remember any x − line is vertical ,so a perpendicular line is a horizontal line that has a slope of $0$ .So,a line perpendicular to $x=4$ must be a horizontal line that crosses the point $(3,-2)$ .The only perpendicular line that fulfills these requirement is $y=-2$ .

Now,the perpendicular line will be $y=-2$ .

Conclusion:

The equation is $y=-2$ .