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WHAT'S MY LINE?

Goal: To write the equation of a line knowing 2 pieces of information about that line.

It is simple to write the equation for any line from a graph or by using some given information. You'll need to use the POINT-SLOPE form of a line:

y - y{short description of image} = m(x - x{short description of image})

m = slope

( x{short description of image} , y{short description of image} ) = coordinates of any point on the line

If you are given this information, just substitute it into the equation

Example 1: m = -4 and (3, 2) is on the line

y - y{short description of image} = m(x - x{short description of image})

y - 2 = -4(x - 3)

y - 2 = -4x + 12

Simplify to "y = " form

y = -4x + 14

What if you only have 2 points on the line?

First calculate the slope, then proceed as above.

Example 2: ( -2, 1) and (3, 4) are on the same line

Recall the slope formula m = (y{short description of image} - y{short description of image} ) / (x{short description of image} - x{short description of image})

In our example, m = (4 - 1) / (3 - -2) = 3/5 or m = (1 - 4) / (-2 - 3) = 3/5 Same result!!

Now finish like example 1. You may use either point in the formula.

y - y{short description of image} = m(x - x{short description of image} ) y - y{short description of image} = m(x - x{short description of image} )
y - 1 = (3/5)(x - -2) y - 4 = (3/5)(x - 3)
y - 1 = (3/5)x + 6/5 y - 4 = (3/5)x - 9/5
y = (3/5)x + 11/5 y = (3/5)x + 11/5
SAME RESULT!

If you only have a graph, choose any 2 points on the graph of the line to work with. Picking the x-intercept and y-intercept as your points makes the calculation simple. Once you have chosen the points, follow the steps in Example 2

{short description of image} (0, 2)
(-3, 0)

Try these problems to perfect your skill in writing the equations of lines. Check by graphing your equations on your calculator to see if the points are on your lines.

1. slope = 2/3 point (6, 7)

2. slope = 4 point (3, 0)

3. points (4, 11) and (5, 9)

4. points (-9, 9) and (0, 1)

5. {short description of image}

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