 Now our job is to write the equation of a line that passes through two given points and We are to do it first in point slope form in slope intercept form and then in standard form Again this this process of starting with slope point slope form moving to slope intercept to standard is a very common practice and Point slope form always seems to be the place that you start. So let's begin there So in order to use the point slope form We need well we need a point and we need the slope So let's pick. Well, we can just pick one of these points. It doesn't matter which one for sake of argument Let's pick this first point as our point for point slope form and Then next we'll need the slope from these two points. Let's use the slope formula Again if that formula isn't in your notes yet, I would recommend you write it in so we'll want y2 minus y1 So let's take y2 minus y1 and We'll divide that by x2 minus x1 and that fraction of course will simplify to negative 2 So now we have our slope So we have our slope of negative 2 and we have a point So all that's left to do is to substitute the values into the point slope form and Then lastly we can simplify the left side. We have y minus negative 4 Of course when you subtract the negative, that's positive. So final answer Y plus 4 is equal to negative 2 times the quantity x minus 2 Next we want the same line, but we want that line in slope intercept form So we'll use point slope form to get to slope intercept So we'll want to take our point slope form And using algebra isolate the y and have the right side equal to mx plus b So first let's use the distributive property on the right side Next we'll subtract 4 from both sides Which leaves us with y is equal to negative 2x Plus 0 and so in y equals negative 2x is our slope intercept form in this case The y-intercept is 0-0 Lastly to put this equation into standard form We'll use the previous slope intercept form and using an algebra will get it into standard form first remind yourself a standard form and so we have the equation y equals negative 2x and We want the y's and the x's to be on the same sides of the equation So we'll add 2x to both sides So we have 2x plus y is equal to 0 and now that's fair game Even though it doesn't look like a b and c while c c is 0 right now But 0 is an integer and so now we're all done This example is finished We had an equation in point slope form We have the same equation in slope intercept form and lastly we have the equation in standard form