 Here we've got another example where we want to find the equation of a line in standard form. However, we're given just two points. Now the usual technique that we've used in previous examples is start with point slope form using algebra change that to slope intercept form and then finally using algebra once again get that into standard form. However, in order to use point slope form we need a point. Well, we have two but we also need the slope and so we'll need to use the slope formula using these two points in order to use this point slope form of the line. So let's find the slope. Do you remember the slope formula? If not, you should test yourself. Make sure you do. Memorize that. That's an important formula to know. So let's take 1 minus negative 5 and we'll divide that by 10 minus 2. So we have 6 eighths, which of course simplifies to 3 fourths, and now we have slope sorry, positive 3 fourths, and then we can pick either one of these two points to put it into point slope form, which of course then we'll use to get slope intercept form, which will then give us standard form. So for point slope form, let's use, let's use this, oh pardon me, let's use this first point 2 negative 5. So put that in a point slope form and now let's work through the algebra to get to standard form. First things first, let's convert point slope form to slope intercept form. So first use the distributor property, distribute 3 fourths times x and times negative 2. Now 3 fourths times x of course is 3 fourths x. 3 fourths times negative 2 is going to give us negative 6 over 4, but negative 6 over 4, that can be simplified instead of 6 over 4, we can call that 3 over 2. And then next we'll want to add 5 to both sides of the equation. And so that leaves us with y equals 3 fourths x. Now let's, let's be a little bit more deliberate about this next one. We have negative 3 over 2 plus 5. Plus 5, in order to add 5 to negative 3 over 2, we want to add common denominators. So instead of adding 5, we could add 10 over 2. And so that should give us way to tick. I made a mistake, didn't I? Do you see where it was? Mistake was right here. Instead of adding 5 to both sides, I should be subtracting 5 from both sides. Sorry about that. So instead of my add 5, I should say minus 5, minus 5, so I should be subtracting 10 over 2. That was close. All right, so y is equal to 3 fourths x minus 13 over 2. There we go. Now we've got slope intercept form. And now what's next is to change that into standard form. So for standard form, we want the x's and the y's to be on both sides of the equation. So since we have positive 3 fourths x, I'll subtract that from both sides of the equation. Then I'll want to get rid of the fractions. Since I've got 3 over 4 and negative 13 over 2, I'll multiply by 4. And the reason I'll choose 4 is 4 is the common multiple of 2 and 4. So I'll multiply by 4 on both sides. And that'll have the net effect of removing those fractions, turning them into integers. So 4 times negative 3 fourths is negative 3. 4 times y, of course, that's just 4y. And then negative 13 over 2 times 4 is essentially like saying negative 13 times 2 without over 2. So that gives us negative 26. And then lastly, standard form, or at least proper standard form, does not include a negative value for the number that's attached to the x. So we'll want to multiply both sides of this equation by negative 1. So negative 1 times negative 3x is positive 3x. Negative 1 times positive 4y is negative 4y. And then negative 26 times negative 1 is positive 26. So there we go. Our final answer, 3x minus 4y is equal to 26.