Chapter 1 Section 2
| Slope® | rise | = | dy | = | y-y |
| run | d x | x-x |
Horizontal or Vertical Lines
| Horizontal Lines ® | Slope is 0 | Equation: y = b |
| Vertical Lines ® | Slope is undefined | Equation: x = a |
Parallel Lines have same slope.
3||3
Perpendicular Lines have opposite slope. 3^ -1/3
Point-slope Form is y-y=m(x-x)
Slope-intercept Form is y = mx+b
Ex:
Line with slope -5/2 and passes through (3,-5)
y+5= -5/2(x-3)
y = -5/2x + 2 1/2
Standard Form is Ax + By = C
Ex:
Find slope and y-int:
6x+2y = 14
Solve for y: 2y = -6x + 14
y = -3x + 7
slope is -3 and y-int is 7
Distance
between two points:
d =
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Absolute Value = { |
x if x ≥ 0 |
| -x if x > 0 |
X and Y intercepts
| Ex.1 8x - 2y = 16 | ||||
| x | - | y | = |
1 |
| 2 | 8 | |||
| x =2 and y = -8 | ||||
FINDING THE DISTANCE FROM A POINT TO A LINE:
Distance from
a point to a line is the perpendicular segment from the point to that line.
Ex: Point (-5,2) is perpendicular to line y = 3x+1
slope of the line is 3 and perpendicular slope is -1/3
y-2= -1/3(x+5) then y = =1/3x+1/3
Set two lines equal
to find the intersection:
3x+1= -1/3x+1/3
3 1/3x = -2/3
x = - 1/5
Find y: y = 3(-1/5)+1
y = 2/5 therefore, the point of intersection is (-1/5, 2/5)
Distance from that point at the original point: (-5,2) is:
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