geduiwelh

2020-11-22

True or False? In Exercises 99 and 100, determine
whether the statement is true or false. Justify your
answer, : 99. The line through (−8,2) and (−1,4) and the line
through (0,−4) and (−7,7) are parallel.

firmablogF

Skilled2020-11-23Added 92 answers

The given statement is False.

Reason: The slope of the line passing through the points (x1,y1) and (x2,y2) is given by

$m=\frac{y1-y2}{x1-x2}$

Using this formula the slope of the line through (−8,2) and (−1,4) is given by

$m1=\frac{2-4}{-8+1}=\frac{2}{7}$

And the slope of the line through (0,−4) and (−7,7) is

$m2=\frac{-4-7}{0+7}=-\left(\frac{11}{7}\right)$

Since, the slopes m1 and m2 are not equal or not proportional, the given lines are not parallel.

Reason: The slope of the line passing through the points (x1,y1) and (x2,y2) is given by

Using this formula the slope of the line through (−8,2) and (−1,4) is given by

And the slope of the line through (0,−4) and (−7,7) is

Since, the slopes m1 and m2 are not equal or not proportional, the given lines are not parallel.