# Help With Coordinate Geometry - The LineI have a test tomorrow (Friday) on The Line and I am just wondering if anyone could help me with the equation of a line. If anyone could give me a few...

Help With Coordinate Geometry - The Line

I have a test tomorrow (Friday) on The Line and I am just wondering if anyone could help me with the equation of a line. If anyone could give me a few examples with answers for me to study and then a few examples that I could try out myself. This would be a great help as I am finding these difficult. Thanks A Million.

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The problems use the different forms of equation of the line such that:

- the slope intercept form: `y = mx + b` (m represents the slope of the line, b represents y intercept)

- the point slope form: `y - y_0 = m(x - x_0` ) (m represents the slope of the line, `(x_0,y_0)` coordinates of a point on the line)

- two points form: `y - y_1 = (y_2-y_1)/(x_2-x_1)(x - x_1) ((x_1,y_1),(x_2,y_2)` represent the coordinates of two points on the line`)`

Hence, if the problem provides the coordinates of two points, located on the line, `(1,2),(3,-5)` you may evaluate its equation such that:

`y - 2 = (5-2)/(3-1))(x -1) => y - 2 = (3/2)(x - 1)`

If theproblem provides the slope of the line, `m=-2` , and the coordinates of a point located on the line, `(1,2)` , you may find the equation of the line, such that:

`y - 2 = -2(x - 1) => y = -2x + 2 + 2 => y = -2x + 4`

Hence, depending on the information provided by the problem, you may evalaute the different forms of equation of the line.

Posted on

I'm assuming you're talking about the Slope Form when we use the equation of a line.

Formula to Use:

y y1 = m(x x1)

Example 1:

For this to work you have to have one point and the slope.

Point 1: (5,4) with a slope of 2

First, fill in your equation with real data:

y - 4 = 2(x - 5)

y - 4  =  2x - 10  (Distributive Property)

Then Solve for y by getting y on one side, but still keeping the equation balanced.

y -4  = 2x - 10

+4  =      +4 (The left side cancels out, the right side is -10 +4=-6)

y      = 2x - 6

You answer would look like this:

The equation of the line is   y = 2x - 6

Here's one more without all the notes.  See if you can follow it.

Point 1 = (-4,3)  and the slope is -3

y y1 = m(x x1)

y - 3   = -3(x - (-4))

y - 3   = -3(x + 4)

y - 3   = -3(x + 4)

y - 3   = -3x  - 12

+ 3   =        + 3

y        = -3x   - 9

The equation of the line is  y = -3x - 9

Here are the steps to remember

-  First, fill in your equation with real data:

-  Then simplify using your properties:

-  Then Solve for y by getting y on one side, but still keeping the equation balanced.

1.)  Point 1 = (-7,2)  and the slope is -5

2.)  Point 1 =  (8,-4) and the slope is 5

3.)  Point 1  =  (6,3) and the slope is 6