# Write an equation in standard form given point slope form of a line So your change in, let me write this. We have a negative eight change in Y, which makes sense. And we've plotted that point there.

## Equation of a line

Notice that all of the y-coordinates are the same. And so what's your slope? So if we find the difference between that Y and this Y, and nine, and it's over the difference between some X on the line and this X, and four. We know that the slope between any two points on this line is going to be negative four. The Point-Slope Formula Given the slope and one point on a line, we can find the equation of the line using point-slope form. And to get this in this form we just have to simplify a little bit of this algebra. Show Solution The x-coordinate of both points is 1. Find the slope using the slope formula. So let's do that.

Are you wondering where that m came from? All you'll need is the point-slope formula for a line. Again to get to this point?

## Standard form equation

Change in Y over change in X. We started at X equals four, so our change in X is six minus four, which is equal to two. Often, the term linear equation refers implicitly to this particular case, in which the variable is sensibly called the unknown. And what we could do is, we could just evaluate well what's the slope between the two points that we know? So now that we have a, now that we know the slope and we know a point, we know a, we actually know two points on the line, we can express this in point-slope form. Point, point-slope form. So we get Y minus 9, we get Y minus nine is equal to our slope, negative four times X minus four. We can use point-slope form. Find the slope using the slope formula. Let's add nine, let's add nine to both sides. Slope is sometimes described as rise over run. And so let's do that. Are you wondering where that m came from? As the slope increases, the line becomes steeper. Again to get to this point?

And we're not in point-slope form or classic point-slope form just yet. Well, your change in X is positive two. Change in Y over change in X. Remember a point is two numbers that are related in some way.

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