how to find standard form using given points?

Question

There is so many steps that I mess them up and mix them together.

Answer 1

Things to know for this problem: Slope: m = (y₂-y₁)/(x₂-x₁)

y-intercept form: y-y₁ = m(x-x₁)

standard form: Ax+By = C

So let's say the given points are (2, 3) and (1,1). I tend to break these into 3 steps.

1. Find the slope. Here we have (3-1)/(2-1) = 2/1 = 2 <---This means m = 2
2. Find the y-intercept form: y -y_{1 =} m(x-x₁). Here you can use either point. Let's use (1,1) to make things easy. Now you plug in your point and you m value. Here we have y-1 = 2(x-1). This gives us y-1 = 2x - 2. Lets simplify this to make it look like y = mx+b by adding 1 to each side. Now we have y = 2x - 1.
3. The final step is to make this look like standard form. This is achieved by putting all the variable on one side and setting them equal to the constant. So we will subtract 2x to obtain -2x+y = -1. Now to make things look nice lets multiple by (-1) to get 2x-y = 1 for your final answer. Hope this helps.