So many topics... Let me address a few:
The x-intercept is where the line crosses the x axis, and the point is (x, 0). Similarly, the y-intercept is where the line crosses the y-axis, at (0,y).
Determine equation of line: Given two points (x1,y1) and (x2,y2), you can determine the slope (referred to as m) of the line by taking the difference in the y values over the difference in the x values (think "change in rise over change in run"):
slope m = (y2 - y1)/(x2 - x1)
You can then plug the slope and one of the points into the point slope form to get an equation for the line:
y - y1 = m(x - x1) . Work it through, combine like terms, and you have your equation.
Similar to point slope form is slope-intercept form, y = mx + b . When the equation is in this form, you can determine both the slope m and the y intercept (0, b) from this equation.
Standard form is Ax + By = C. With a little manipulation, you can work this into slope intercept form.