- Coordinate systems are formed by the intersection of two lines called axes. The horizontal axis is called x, while the vertical axis is called y.
- Coordinate points are named by an ordered pair (x,y).
- Slope: defined as the vertical change divided by the horizontal change (or RISE/RUN)
Slope formula: y2 – y1 x2 – x1
- Types of slopes
- Slopes that rise from left to right are positive.
- Slopes that fall from left to right are negative.
- Horizontal lines have a slope of 0.
- Vertical lines have slopes that are undefined.
- Slope-intercept form of an equation: y = mx + b where m = slope and b = y-intercept
- Standard form of an equation: Ax + By + C = 0 where A,B,C are integers and A>0.
- Parallel lines have the same slopes while perpendicular lines have negative reciprocal slopes. (e.g. slope of line 1 = 3, slope of line 2 = 3, slope of line 3 = -1/3; therefore line 1 and 2 are parallel, line 1 and 3 are perpendicular)
- The distance between any two points P1(x1,y1) and P2(x2,y2) is given by this formula:
- When M is the midpoint of a line segment having endpoints P1(x1,y1) and P2(x2,y2), the coordinates of M are:
- To find the equation of a line given the slope and 1 point: (e.g. find the slope of the line with slope 2/3 and point A(3,4)
1. Pick some other point on the line and call it (x,y) 2. Use the given point and (x,y) with the slope in the slope formula:(y-4) = 2(x-3) 3 3. Cross multiply and simplify:2(x-3) = 3(y-4)2x – 6 = 3y – 12 4. Rearrange into standard form of equation:2x – 3y + 6 = 0
- To find the equation of a line given two points: (e.g. find the equation of the line with points A(5,-4) and B(3,2))
1. Find the slope using the given points and the slope formula
(3 – 5)
=-3 2. Follow the above steps 1 – 4 using one of the given points and the slope.