Line Joining 2 Points

Algebra: Lines Help


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The easiest way to show you how to do this is by working out an example.

Example: Find the equation of the line joining (-2,8) and (-7,-5).

The first thing we do is find the slope. To do that you have to know how to subtract integers. Remember that the slope is rise over run which is the same thing as saying the change in y over the change in x. If we use the formula y = mx + b, where m is the slope and b is the y-intercept, we get

eq001

eq002

Of course, if we had done it the other way, we would have ended up with the same answer.

So, now our equation is:

Eq003

Now we have to solve for the y-intercept. We do that by picking one of our points, and plugging the values into the equation. Let's do it with (-2, 8):

Eq004

Eq005

Eq006

Eq007

Eq008

Eq009

As you can see, it helps to know how to multiply a fraction and a whole number and subtract a fraction from a whole number.

So, our final equation is:

eq010

If you're not a big fan of fractions, you can multiply both sides of the equation by 5 to get 5y = 13x + 66. If you want the variables on one side and the y-intercept on the other, we would have 5y - 13x = 66 which is the form the equation is usually written in when we are solving for the intersection point of 2 lines.

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Algebra: Line Help

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