Question

identify which lines are parallel: y=-x; y-3=-1(x+9); y-6=1/2(x-14);y+1=1/2x

Answer 1

Parallel lines have the same slope, so if you can get them all into Slope-Intercept form, you will be able to determine which lines have the same slope.

Recall: Slope-Intercept form is written y=mx+b ; where m is the slope and b is the vertical intercept.

y=-x is already in slope-intercept form ; the slope is -1

y-3=-1(x+9)

First use the distributive property on the right side to get rid of the parenthesis

y-3=-x-9

Then add 3 to both sides to get the y by itself

y=-x-6 ; the slope is -1

y-6=1/2(x-14)

Same thing as above for this one, distribute the 1/2

y-6=1/2x-7

Then add 6 to both sides

y=1/2x-1 ; the slope is 1/2

y+1=1/2x

Here, you just have to subtract 1 from both sides

y=1/2x - 1 ; the slope is 1/2

So, to answer the question: The first two equations you gave each have the same slope, and the second two equations you gave each have the same slope.

Answer 2

y=-x; y-3=-1(x+9) <---- these two are parallel

y-6=1/2(x-14);y+1=1/2x <---- and these two are parallel