A bit confused on this:

1. Find the equation of the line between the points (9, -9) and (-5, -2).

m=y2-y1 -2 - -9 7 = -1

--------- (over) --------- ---- ----

x2-x1 -5 - -9 -14 2

y=-1/2x+b ... How would I find b, the y-intercept then?

2. Find the equation of the line with an x-intercept of -2 and a y-intercept of 7.

That's the points (-2, 0) and (0, 7), so m=y2-y1/x2-x1 again, or 7-0/0--2 = 7/2....which would be y=7/2x+b and the y-intercept is 7 so the final equation would be y= (7/2) x + 7 ? just checking.

Mr F says: Correct. Note the brackets ....
3. Find the equation of the line that has the same x-intercept as x-4y=3 and the same y-intercept as 2x-3y=9.

x-4y=3 rearranges to x=4y+3, and to find the x-int you would substitute 0 in right for y so x=4(0)+3 or x=4+3, or x=7... so the x-intercept is 7.

Mr F says: 4(0)+3 = 0 + 3 = 3.
For the y-intercept, 2x-3y=9 you substitute 0 in for x, so 2(0)-3y=9 would be 0-3y=9 or just -3y=9... or y=-3.

Mr F says: Correct.
I guess the equation so far would be y=mx-3... but I don't know how I would find the slope at this point to finish the equation.

Mr F says: Substitute (3, 0) into y = mx - 3 and solve for m.
4. Finally... (the most important question) If A(1,2), B(-2,5) and C(3, 4), find the equation of the line perpendicular to AB and through C.

I know the slope of the line perpendicular to something is the negative reciprocal... but I don't know what to do here.

If I found the slope of A and B, that would be 2-5/-2-1 or -3/-3 or 1

Mr F says: NO. (2 - 5)/(1 -(-2)) = -3/3 = -1.
I guess, so then would the slope of the new line be -1/2?

Mr F says: No. The gradient of the perpendicular is (and you should know this) the negative reciprocal of -1, that is, 1.
What impact does "through C" have? The equation so far if that's right of the new line would be y=-1/2x+b... b being the y-intercept again, but I don't know what to do from this point on.

Mr F says: Substitute m = 1 to get the required equation as y = x + c. Now substitute the given point (3, 4) and solve for c.
Thanks for reading! My math skills aren't great... or even "good" for that matter