Chapter 8: Slopes and Equations of Lines Flashcards
Negative slope
As the x values increase, the y values decrease
Positive Slope
As the x values increase, the y values increase
Zero Slope
As the values of x increase, the values of y remain the same (horizontal)
No slope (undefined)
The values of x remain the same, as the y values increase (vertical)
Point slope formula
Y-b
=m
X-a
To find the equation of a line given two points on the line:
- Find the slope of the line using the coordinates of the two given points.
- Let P(x, y) be any point on the line.
- Write a ratio that expresses the slope of the line in terms of the coordinates of P and the coordinates of one of the given points.
- Let the slope found in the third step be equal to the slope found in the first step.
- Solve the equation for y
Midpoint
the point of a line segment that divides the segment into 2 congruent segments
Midpoint formula
(x+x, y+y)
2 2
Two lines that are perpendicular have slopes that are
Negative reciprocals
Proofs Involving Special Cases
when the coordinates of the endpoints of a segment of the vertices of a polygon are given as ordered pairs of numbers, we are proving something about a specific segment or polygon.
Proofs of General Theorems
when the given information is a figure that represents a particular type of polygon, we must state the coordinates of its vertices in general terms using variables.
Orthocenter
the point where the altitudes of a triangle intersect
The altitudes of a triangle are
Concurrent
Slope
y-y
x-x
How to find the othrthocenter
- Graph the triangle/polygon
- Pick a side
- Find the slope of that side
- Find the negative reciprocal
- Graph the line using the negative reciprocal slope starting at the extra point
- Repeat for all sides
