Is the line through points p(-7,8) and q(-5,-6) parallel to the line throuh points r(3,-5) and s(-2,0)? explain. a. no, one line has slope, the other has no slope b. no, the lines have unequal slopes. c. yes, lines have equal slopes. d. yes, the lines are both vertical.

I'm going to use the slope formula which is
m = (y2 - y1)/(x2 - x1)
where (x1,y1) and (x2,y2) are the two points the line goes through

Slope of line PQ
m = (y2 - y1)/(x2 - x1)
m = (-6 - 8)/(-5 - (-7))
m = (-6 - 8)/(-5 + 7)
m = (-14)/(2)
m = -7
The slope of line PQ is -7

Slope of RS
m = (y2 - y1)/(x2 - x1)
m = (0 - (-5))/(-2 - 3)
m = (0 + 5)/(-2 - 3)
m = (5)/(-5)
m = -1
The slope of line RS is -1

Because the slopes are NOT equal (one is -7 and the other is -1), this means the lines are NOT parallel.



Choice B) No, the lines have unequal slopes

Slope formula : (y2 - y1) / (x2 - x1)

(-7,8),(-5,-6)
slope = (-6 - 8) / (-5 - (-7) = - 14/(-5 + 7) = -14 / 2 = -7

(3,-5),(-2,0)
slope = (0 - (-5) / (-2 - 3) = (0 + 5) / -5 = -5/5 = -1

B. no, the lines have unequal slopes