Alright, you're dealing with a lot of stuff here. A couple of formulas to get you rolling:
Slope-intercept: y = mx + b, and m is the slope and b is the y-intercept.
Point-slope: (y - y1) = m(x - x1), and (x1, y1) is any given point and m is the slope.
Standard form: Ax + By = C
Slope: (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are given points.
For number 1, you want to take the points you were given and find your slope using that last formula. Once you get the slope, you want to take it to point-slope form and let m = the slope. Then pick one of the two given points and plug it as (x1, y1), then change it to slope-intercept form (solve for y). That'll give you one of your answer choices.
For number 2, all they want you to do is rearrange your given formula to match standard form. With standard form, all you have to do is move your variables to one side and let your constant hang out on the other side. For y = 2x - 7, you'd get -2x + y = -7, but to clean that up, you can multiply the entire equation by -1 to flip all the signs. Then you have 2x - y = 7.
For number 3, they gave you the answer in standard form, and now your job is to convert that back into slope-intercept form. All you have to do here is solve for y, and you'll find that you get an equation that is exactly of the form y = mx + b!
For number 4, you just have to know what y = mx + b means. Remember m is slope and b is the y-intercept, so for y = 4 - 3x, you can rearrange it to read y = -3x + 4 and see that your "m" is -3. Or if it's easier, just look for the number "attached" to x (called a coefficient, but I don't know if you're using those terms yet).
For number 5, once again, you just have to use the slope formula. (y2 - y1)/(x2 - x1), and you should get one of those answer choices.
For number 6, take a look at that graph. Start at the y-intercept because it's easiest. From the y-intercept, go up one over one, up one over one, and follow the slope of the line. You want to find the rise over run. This is pretty difficult to explain in words, so I'd recommend just looking up a video on how to find the slope from a graph.
For number 7, you're doing something pretty similar to number 4. Your teacher just wants to know what you know what slope-intercept form means. Remember that in y = mx + b, m is the slope, and b is the y-intercept. So for y = 2x - 7, 2 is your slope, and -7 is your y-intercept.
For number 8, they throw you a curveball and want to know the x-intercept. You can get this a few ways. If you like graphing, graph the equation, and see where this line crosses the x-axis. If you don't like graphing, then just solve for x and kinda do what you did for number 7. I'll show you how to handle it:
y = -5x + 3 ... subtract 3 from both sides
y - 3 = -5x ... divide both sides by -5
(-1/5)y + (3/5) = x
Now, this isn't in y = mx + b format; we did it backwards and solved for x. But it works the same way. The x-intercept will be the number being added to (-1/5)y -- basically, it's whatever number that isn't attached to a variable once you solve for x. So your x-intercept is 3/5.
