Chapter ISG, Problem 4.1.4P

a.

To determine

To evaluate the given statement.

Answer to Problem 4.1.4P

The two lines are not perpendicular

Explanation of Solution

Given information:

One line goes through (-6, -2) and (2, 10)

Other graph is $3x-2y=10$

Formula Used:

Product of slopes of two perpendicular slope is -1.

Equation of line,

  $y=mx+c$

Formula of slope is,

  $m=\frac{y2-y1}{x2-x1}$

Calculation:

For the slope of line, substituting the value in slope formula,

  $m=\frac{10-(-2)}{2-(-6)}$

So,

  $m=\frac{10+2}{2+6}$

On solving,

  $m=1.5$

Hence, slope is 1.5

Converting the graph equation in equation of line format,

Shift left-hand side values to right-hand side,

  $-2y=10-3x$

Cross-multiplying both sides,

  $y=\frac{-3x+10}{-2}$

On solving,

  $y=\frac{3}{2}x-5$

On solving,

  $y=1.5x-5$

Comparing it with the equation of line,

Slope is 1.5

Multiplying both the slopes,

  $=1.5\times 1.5$

On solving,

  $=2.25$

Since, the product of the two slopes is 2.25 and not -1.

Therefore, the two lines are not perpendicular.

Conclusion:The two lines are not perpendicular

b.

To determine

To evaluate the two lines

Answer to Problem 4.1.4P

The given two lines are not parallel

Explanation of Solution

Given information:

The line goes through (7, -10) and (3,-2)

Another line is $2x-y=-5$

Formula Used:

Two parallel lines have the same slope (m).

Formula of slope is,

  $m=\frac{y2-y1}{x2-x1}$

Equation of line is,

  $y=mx+c$

Calculation:

For the slope of line one, substituting the values in the slope formula,

  $m=\frac{-2-(-10)}{3-7}$

So,

  $m=\frac{-2+10}{-4}$

On solving,

  $m=-2$

Hence, the slope of line one is -2.

Converting the equation of line two in the form of $y=mx+c$ ,

Shifting left- hand side value to right- hand side,

  $y=2x+5$

Comparing with $y=mx+c$ ,

Hence, slope of line two is 2

Comparing the slopes of the two lines,

The slopes of the two lines are not equal as slope of line one is 2 and slope of line two is -2.

Therefore, the lines are not parallel

Conclusion:The given two lines are not parallel

c.

To determine

To identify the mistake in the statement.

Answer to Problem 4.1.4P

The two lines are not parallel because the two lines have a common point.

Explanation of Solution

Given information:

Line1 goes through (1,-4) and (5,-6)

Line2 goes through (2,-7) and (5,-6)

Formula Used:

Two parallel lines do not intersect each other.

Calculation:

The point lines have a common point, that is (5,-6), hence the two lines intersect at that point.

Hence, the two lines are not parallel and Alonae is wrong.

Conclusion: The two lines are not parallel because the two lines have a common point.