General Form of equation of a line
Slope (steepness) Formula
- m= y2-y1 x2-x1
- m= rise = vertical change run horizontal change
How do you read the graph?
Left to right
m<0 negative, hence y=b
zero (m=0) hence y=b
Undefined, hence x=a
Slope intercept form equation
slope = m
coordinate y= b
How do we write the equation for slope intercept form?
Isolate y variable so that it is
y= slope (x) + b from given equation
What is the y-intercept always equivalent to?
the y coordinate
Point slope formula
Used if you have only one point and the slope
(does not work for verticle lines)
How do you find the equation of a line given 2 points?
Use the points to find the slope, and then plug it into the point-slope formula
How do you tell if lines are parallel
They must have the same slope
How do you find the equation of a parallel line?
- 1) write slope intercept form
- 2) identify the slope given (parallel lines have same slope)
- 3) substitute slope into equation of the line
- 4) substitute in variables (coordinates given)
- 5) since b is the only variable left, SOLVE FOR B
What is unique ( and always true) about perpendicular slopes?
The slopes' of the two lines will always be negative reciprocals of eachother
Which two types of lines do not share the perpendicular slope property?
- horizontal, m=0
- vertical, slope undefined
How do you find the equation of a perpendicular line?
- 1) Identify the slope of the given line
- 2) identify its reciprocal to find the slope that is perpendicular to given line
- 3) Write equation of the line we are looking for in slope-intercept form y=m2x+b
- 4) substitute the reciprocal slope back into equarion
- 5) plug in coordinates
- 6) since b is the only variable left, SOLVE FOR B