11) Is the line through (-4,-6,1) and (-2,0,-3) parallel to the line through (10,18,4) and (5,3,14)?

Name points:

A (-4, -6, 1)

B (-2, 0, -3)

C (10, 18, 4)

D (5, 3, 14)

Line through points A and B is parallel to line through points C and D iff vectors AB and CD are scalar multiples of each other (or scalar multiples of a common vector)

AB = (-2+4, 0+6, -3-1) = (2, 6, -4) = 2 (1, 3, -2)

CD = (5-10, 3-18, 14-4) = (-5, -15, 10) = -5 (1, 3, -2)

So, yes the lines are parallel

Hi: given: mx+b= y , (-3,-11) , 2x-y= 4 . we want a line equation that passes (-3,-11) and is parallel to 2x-y= 4 2x-y=4 2x-y+y= 4+y 2x=4+y 2x-4= 4+y-4 2x-4 =y since the slope of another parallel line is the same for line above ( 2x) So: mx+b = y - Standard slope intercept line equation 2x+ b= y - substituting for the slope 2(-3)+b= -11 - substituting for x and y -6+b=-11 - Multiplication 6=-6+b=-11+6 - Adding the additive inverse of a number to both sides of the equation to move it to the other side of it b= -5 - Addition proof : Prove that the following equation 2x-5 = y go through the points (-3,-11) when x = -3 2x-5= y - Derived equation from the above 2(-3)- 5 =-11 - Substitution -6- 5= -11 - Multiplication -11 = -11 - Addition it equals and checks Therefore the following equations is true 2x-5 = y goes through the points (-3,-11) when x = -3 proof : prove that 2x-5= y and 2x-4=y are parallel lines mx+b= y Standard slope intercept line equation 2x-4= y 2x-5= y Derived or stated equations from the above -1(2x-4) = -1*y 2x-5= y - Multiplying a number (-1) to both side of a equation to a variable to change it from a postive value to a negative value -2x+4= -y 2x-5= y ---------------- - Multiplication and addition of terms 0x+1= 0y 1= 0 - Addition It does not equal or check So there is no solution possible; because those two line are parallel and thus they have no interception points so your answer is #2