There are two common forms for the equation of a (straight) line.
The standard form is ax + by = c. The slope of the line is -a/b, the x-intercept is c/a, the y-intercept is c/b.
Another common form is the slope-intercept form, it looks like this: y = mx + b. (Note that this b is different from the one in the standard form.) This form has the advantage that the slope can be easily recognised - it is m. The y-intercept is b, the x-intercept is -b/m. It has the disadvantage that vertical lines (lines parallel to the y-axis) cannot be represented in this form.
If you are given a point on a line (x0, y0), and its slope (m), the equation of the line can be found: y - y0 = m * (x - x0). If you are given two points on the line, the equation of the line is (y - y0) / (y1 - y0) = (x - x0) / (x1 - x0). If you are given the x-intercept (v) and y-intercept (w), the equation of the line is (x / v) + (y / w) = 1