# Write an equation for a line given two points

That's 0 coma 13 over 3 or 0 coma 4 and 1 thirds. And all it does is tell us the change in y you go from this point to that point We have to go down, our rise is negative we have to go down Let's quickly review the steps for writing an equation given two points: 1. Based on your equation, how many participants are predicted for the fifth year?

Write an equation that can be used to predict the amount of participants, y, for any given year, x.

Remember a point is two numbers that are related in some way. All we need to do is substitute!

You can look at that visually there or you can use this formula same exact idea, our ending x-value, our ending x-value is 5 and our starting x-value is negative 1.

Now you will have to read through the problem and determine which information gives you two points. So this y-intercept right over here.

### Write an equation for a line given two points

So it takes us one to go to zero and then five more. And even with my very roughly drawn diagram it those looks like this. Now that we have an equation, we can use this equation to determine how many participants are predicted for the 5th year. And all it does is tell us the change in y you go from this point to that point We have to go down, our rise is negative we have to go down So we literally just substitute this x and y value back into this and know we can solve for b. That is equal to negative So m, or the slope is the change in y over the change in x. So we have 6 is equal to positive five thirds plus b. You can see here the slope is downward because the slope is negative. So we started at x is equal to negative 1, and we go all the way to x is equal to 5. And the first point is -1,6 So -1, 6. And now we can subtract 5 thirds from both sides of this equation.

So negative 1 coma, 1, 2, 3, 4 ,5 6. And to do that, we can use the information that we know in fact we have several points of information We can use the fact that the line goes through the point -1,6 you could use the other point as well. That is equal to negative And we can write these as mixed numbers.

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