Chapter ISG, Problem 4.2.2P

a.

To determine

To form an equation of line.

Answer to Problem 4.2.2P

The equation of line is, $y+1=\frac{1}{5}(x-2)$

Explanation of Solution

Given information:Line passes through point (2, -1)

Line is perpendicular to line2, which is,

  $5y-x=5$

Formula Used:

Equation of line is,

  $y-y1=m(x-x1)$

And

  $y=mx+c$

Product of slope of two perpendicular lines is -1.

Calculation:

In line2,

Shifting left hand side values to right hand side,

  $5y=x+5$

Cross-multiplying both sides,

  $y=\frac{x+5}{5}$

On solving,

  $y=\frac{1}{5}x+1$

Comparing the equation and equation of line in terms of slope and intersect,

Slope of the line is,

  $\frac{1}{5}$

Substituting the values in line of equation in in terms of point and slope,

  $y-(-1)=\frac{1}{5}(x-2)$

On solving,

  $y+1=\frac{1}{5}(x-2)$

Conclusion: The equation of line is, $y+1=\frac{1}{5}(x-2)$

b.

To determine

To form an equation of line.

Answer to Problem 4.2.2P

The equation of line is $y-5=\frac{-2}{5}(x+2)$

Explanation of Solution

Given information:

x	y
-5	7
-2	5
1	3
4	1

Formula Used:

Equation of line is,

  $y-y1=m(x-x1)$

Slope is,

  $m=\frac{y2-y1}{x2-x1}$

Calculation:

For slope, substituting the values,

  $m=\frac{5-7}{-2-(-5)}$

So,

  $m=\frac{5-7}{-2+5}$

On solving,

  $m=\frac{-2}{3}$

Substituting the values in the equation of line,

  $y-5=\frac{-2}{5}(x+2)$

Conclusion: The equation of line is $y-5=\frac{-2}{5}(x+2)$

c.

To determine

To form an equation of line.

Answer to Problem 4.2.2P

The equation of line is $y+4=\frac{2}{5}(x-10)$

Explanation of Solution

Given information:

  

Formula Used:

Equation of line is,

  $y-y1=m(x-x1)$

Slope is,

  $m=\frac{y2-y1}{x2-x1}$

Calculation:

For slope, substituting the values,

  $m=\frac{-4-(-8)}{10-0}$

So,

  $m=\frac{-4+8}{10}$

On solving,

  $m=\frac{2}{5}$

Substituting the values in the equation of line,

  $y-(-4)=\frac{2}{5}(x-10)$

On solving,

  $y+4=\frac{2}{5}(x-10)$

Conclusion: The equation of line is $y+4=\frac{2}{5}(x-10)$