AP Calc Notes: L-1 Lines and Slopes
5 Sizes of Numbers Video
General equation of a line: Ax + By + C = 0 where A, B not both 0.
Slope-intercept form of a line: y = mx + b
Special cases, write the slope for each:
1. Horizontal line (y = b)
2. Vertical line (x = a)
3. Direct variation (line through the origin; y = mx)
Point-slope form:
Let ( x1 , y1 ) be a known point on the line and m be the known slope.
Δy
y - y1
=
=m
Δx
x - x1
Or
Slope = m
•
( x, y )
•
( x1 , y1 )
y - y1 = m(x - x1 )
→
y
y = m(x - x1 ) + y1
x
Slope formula
y - y1
Δy
= 2
=m
Δx
x2 - x1
Parallel lines have slopes that are ________________________.
Perpendicular (normal) lines have slopes that are ____________________________.
Ex. Write the equation of the line passing through (-2, -1) and (2, -3).
Ex. Write the equation of the line perpendicular to the previous line and passing through (-2, -1).
Page 8/44, read problem, estimate slopes. What determines a ‘best’ insulator?