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Point-slope form linear equations Video transcript So what I've drawn here in yellow is a line. And let's say we know two things about this line.
We know that it has a slope of m, and we know that the point a, b is on this line. And so the question that we're going to try to answer is, can we easily come up with an equation for this line using this information? Well, let's try it out. So any point on this line, or any x, y on this line, would have to satisfy the condition that the slope between that point-- so let's say that this is some point x, y.
It's an arbitrary point on the line-- the fact that it's on the line tells us that the slope between a, b and x, y must be equal to m. So let's use that knowledge to actually construct an equation.
So what is the slope between a, b and x, y? Well, our change in y-- remember slope is just change in y over change in x. Let me write that.
Slope is equal to change in y over change in x. This little triangle character, that's the Greek letter Delta, shorthand for change in. Our change in y-- well let's see.
If we start at y is equal to b, and if we end up at y equals this arbitrary y right over here, this change in y right over here is going to be y minus b. Let me write it in those same colors.
So this is going to be y minus my little orange b. And that's going to be over our change in x. And the exact same logic-- we start at x equals a. We finish at x equals this arbitrary x, whatever x we happen to be at.
So that change in x is going to be that ending point minus our starting point-- minus a. And we know this is the slope between these two points.
That's the slope between any two points on this line. And that's going to be equal to m. So this is going to be equal to m. And so what we've already done here is actually create an equation that describes this line. It might not be in any form that you're used to seeing, but this is an equation that describes any x, y that satisfies this equation right over here will be on the line because any x, y that satisfies this, the slope between that x, y and this point right over here, between the point a, b, is going to be equal to m.
So let's actually now convert this into forms that we might recognize more easily. So let me paste that. So to simplify this expression a little bit, or at least to get rid of the x minus a in the denominator, let's multiply both sides by x minus a.
So if we multiply both sides by x minus a-- so x minus a on the left-hand side and x minus a on the right.©d 82P0k1 f2 T 1K lu9t qap 2S ho KfZtgw HaTrte I BL gLiCQ.e R xA NlOlh JrKi0gMh6t8sq YrCenshe Rr8vqeed Y JMGapdQeX TwGiRt VhW 8I 2n fDiPn 8iDtEep QAVlVgue3bjr vaV Y Equations of lines come in several different forms.
Two of those are: slope-intercept form; where m is the slope and b is the y-intercept. general form; Your teacher or textbook will usually specify which form you should be using. In the last lesson, I showed you how to get the equation of a line given a point and a slope using the formula Anytime we need to get the equation of a line, we need two things.
Point-slope refers to a method for graphing a linear equation on an x-y axis. When graphing a linear equation, the whole idea is to take pairs of x's and y's and plot them on the graph. When graphing a linear equation, the whole idea is to take pairs of x's and y's and plot them on the graph.
After completing this tutorial, you should be able to: Find the slope of a line that is parallel to a given line. Find the slope of a line that is perpendicular to a given line.
Algebra 1 Here is a list of all of the skills students learn in Algebra 1! These skills are organized into categories, and you can move your mouse over any skill name to preview the skill.