# 9.5.4. Equation of the Straight Line Given Its Slope and Its y–Intercept

is a triangle in which , , and , where is the midpoint of , and , where intersects at . Find the equation of the straight line in the form of .

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### Example

is a triangle in which , , and , where is the midpoint of , and , where intersects at . Find the equation of the straight line in the form of .

### Solution

First, find the coordinates of .

For any 2 points and , the coordinates of the midpoint of the line joining the points are

is the midpoint of , so substituting the coordinates of and in the above gives us the coordinates of .

Next find the slope of .

We know that the slope, , of a line passing through 2 points and is given by

We know that , so we can find their slope by substituting the coordinates of and in the above.

Then find the equation of .

For straight line graphs, where is the slope and is the -intercept.

The slope is 1 and the coordinates of satisfy the equation

Therefore,

So, the equation of the line is

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