Are my answers correct regarding parallel lines, points, etc.

Are the points (2,1) (3,3) (4,5) collinear?
Yes

Are the lines 2x - 3y = 1 and 2x + 3y = 2 intersecting or parallel?
Parallel

Find b so that the two lines given are parallel: 3x + y = 1 and bx - y = 3
B = -3x + 4 all divided by 1

This problem I can't figure out. Please help: Find a so that the two lines given are parallel: 5x + 2y = 6 and 3x - ay = 4

Thank you so much! Give me a link to your question and Ill answer it as well.

Are the points (2,1) (3,3) (4,5) collinear?
Yes

Correct.

They are all on the same line: y = 2x − 3

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Are the lines 2x − 3y = 1 and 2x + 3y = 2 intersecting or parallel?
Parallel

Incorrect.

First line has slope 2/3, second line has slope −2/3. Parallel lines have same slope. These are not parallel lines, therefore they are intersecting (at point (3/4, 1/6))

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Find b so that the two lines given are parallel: 3x + y = 1 and bx − y = 3
B = −3x + 4 all divided by 1

Incorrect.

First line has slope = −3, second line has slope = b.
To be parallel, we must set slopes equal to each other
Therefore b = −3 (that's it!)

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This problem I can't figure out. Please help: Find a so that the two lines given are parallel: 5x + 2y = 6 and 3x − ay = 4

First line has slope −5/2
Second line has slope 3/a
To be parallel, we must set slopes equal to each other
3/a = −5/2
−5a = 6
a = −6/5

Incorrect>>>>Are the lines 2x - 3y = 1 and 2x + 3y = 2 intersecting or parallel?

solve for y in each you get
y = 2/3x - 1/3
y = -2/3x + 2/3

slopes are not the same they intersect

Incorrect >>Find b so that the two lines given are parallel: 3x + y = 1 and bx - y = 3

solve for y

y = -3x + 1
y = bx - 3