How to Write Equations in a Slope-Intercept Parametric Equation

Hi, I'm Rachel, and today we're going to be going over how to write equations in a slope intercept parametric equation. So when we're doing this, we have two equations, one is an x equals and the other is a y equals, and both include the value, the variable t. So we can have like x equals one plus t and y equals two plus t. Now, we want to use that t to substitute. So we're gonna solve for t and substitute it in one of the equations. So, let's start with this one and we'll substitute it in this one. So, we have let's solve for t, so we subtract two on both sides to isolate the t, and we get t equals y minus two. Now we're going to take this value for t and substitute it in this first equation. So we get x equals one plus y minus two, see we're just substituting that for t. So, when we combine that, we get x equals y minus one. Right? So now we're going to add 10 to both sides, that's something you do when you're doing slope intercept parametric equations. So you add 10 to both sides, that's the next step. Then x plus 10 equals y minus one plus 10. That simplifies to x plus 10 equals y plus 9, and then we're just going to solve for y so that we get it into the form y equals mx plus b, because that's the slope intercept form. So let's solve for y by subtracting nine, and I'll bring it up here, we get y equals x minus one. And there is our form, perfect slope intercept form, y equals mx plus b, and we've solved for a slope intercept parametric equation. I'm Rachel and thank you for learning with me today.