I will explain how to obtain the equation of a line in a different post, as well as a more detailed explanation of both slope-intercept form and standard form.
Slope-intercept form is the common way of expressing an equation of a line, and it takes the general form:
y = mx + b
(y - y1) = m(x - x1)
Plugging values into this equation, you will find it quite simple to rearrange it to obtain the slope-intercept form of the equation.
Standard form looks a bit different still, where the x and y variables are written on the same side, and A, B, and C are all coefficients:
Ax + By = C
The general strategy of converting slope-intercept form to standard form (or by extension, converting point-slope form to standard form) is to combine and simplify to rearrange the equation so that your x and y variables (with their coefficients A and B) are on one side, and the constant value (C, the terms without an x or a y in them) on the other side of the equals sign.
Here is an example of this type of question you might see.
y = 10x - 20 (rearrange so x and y are on the same side)
A = 10, B = (-1), C = 20
It is important to note, as in this example, the value for B is negative! This is because the standard form has a PLUS in it. Pay close attention to the sign in your answer! So, more explicitly, the standard form of this equation could be seen as 10x + (-y) = 20.
Another point to consider is that during your simplification of the answer, you may end up with fraction coefficients. In this case, it is smart to multiply everything (both sides!) by the value in the denominator (to remove it from the denominator). Mathematically, if you are doing the same thing to both sides, you aren't really changing anything, which is what makes this allowed. Keeping all numbers as whole numbers and avoiding fractions where possible is a common practice.
If you want to go the other way, and convert from standard form to point-slope form or slope-intercept form, it is basically just the reverse of what we did here. Try it with the above example to see for yourself. Leave me a comment below if you would like additional examples or clarifications. Please +1 this post below if it was helpful.