- A, B, C are integers (positive or negative whole numbers)
- No fractions nor decimals in standard form.
- Traditionally the "Ax" term is positive.
4x-y-7=0
Add 7 to both sides.
4x-y=7 Standard Form
If theres a fraction...
3x+9=7/2y
Multiply everything by the denominator in the fraction
6x+18=7y
Subtract 6x from both sides
7y-6x=18
Point-Slope Form
(y-y(sub 1))=m(x-x(sub 1))
Helps you find the equation of a line given slope and coordinates.
Find the equation of a line with a slope of 4 and passes through the point (1,6).
(y-6)=4(x-1)
y-6=4x-4
y=4x-2
The end result is the equation of a line. In written form its called slope-intercept form.
The 4x is the slope.
The -4 is the y-intercept.
Slope
Change in y over change in x, aka the rise and run of coordinates.
Written as...
y(sub 2) - y (sub 1)
m= -------------------
x(sub 2) - x (sub 1)
for example: (4,6) (2,5)
5-6)/(2-4)
-1/-2
1/2 would be the slope of the coordinates.
Types of slopes
Undefined
Written as (x,0)
0 slope
Written as (0,y)
Continuous
A continuous function's line has no breaks or jumps in it.
Non-continuous
A non-continuous function's line has jumps or breaks in it.
Parallel Lines and their slopes
You can tell two lines are parallel by their slopes in their equations.
If the slopes are the same, they are parallel.
Perpendicular Lines and their slopes
You can tell two lines are perpendicular by their slopes as well.
If the slopes are opposite reciprocals of each other, they are perpendicular.
4/5x+7=y
-5/4x would be the opposite reciprocal
Quadrants
4 Quadrants
1- (+,+)
2- (-,+)
3- (-,-)
4- (+,-)
The vertical line is the Y axis.
The horizontal line is the X axis.
A line is the path of one point moving.
The origin is where he X and Y axes meet.
A coordinates is written as (x,y).