Question

D22: One line passes through the points (−12,16) and (−1,38). A second line has the equation 2y+x=23. Are these lines parallel, perpendicular, or neither? Discuss your solution strategy and then implement it to demonstrate your answer.

Answer 1

compare the slopes

2y + x = 23 -- find the slope by putting it in y = mx + b form, and m is your slope.
2y = -x + 23
y = -1/2x + 23/2
slope is -1/2

given 2 points, we can use the slope formula to find the slope
slope = (y2 - y1) / (x2 - x1)
(-12.16) x1 = -12 and y1 = 16
(-1,38) x2 = -1 and y2 = 38
now we sub
slope = (38 - 16) / (-1 - (-12)
slope = 22/(-1 + 12)
slope = 22/11
slope = 2

so our slopes are -1/2 and 2

parallel lines will have the same slope.
perpendicular lines will have negative reciprocal slopes. All that means is " flip " the slope and change the sign. For example, you have a slope of 4, which is the same as 4/1, if you " flip " the slope and change the sign, -1/4, it is perpendicular.

so what do you think ?