# 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.

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

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.

mrbakertheteacher | Elementary School Teacher | (Level 1) Valedictorian

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