CALCULUS - CHAPTER 0.1
LINES • EXAM-FOCUSED HANDWRITTEN STUDY NOTES
REVISION MAP
Core lecture focus: slope, equations of lines, graphing, horizontal/vertical
lines, parallel & perpendicular lines, angle of inclination, and distance
between two points.
KEY IDEA
The lecture emphasizes that strong algebra and trigonometry skills are
essential preparation for calculus.
1
, 1. LINES & SLOPE
• A line is straight, has infinitely many points, does not curve, and does not
end.
• To graph a specific line, two points are enough.
• A line can also be determined from one point plus its slope.
• Slope describes how a line rises or falls.
FORMULA
m = rise/run = Δy/Δx
For two points (x₁, y₁) and (x₂, y₂):
m = (y₂ - y₁) / (x₂ - x₁)
REMEMBER
Keep coordinates paired: if a point supplies x₁, the y-coordinate from that
same point must be y₁. Either point may be chosen as Point 1.
2
LINES • EXAM-FOCUSED HANDWRITTEN STUDY NOTES
REVISION MAP
Core lecture focus: slope, equations of lines, graphing, horizontal/vertical
lines, parallel & perpendicular lines, angle of inclination, and distance
between two points.
KEY IDEA
The lecture emphasizes that strong algebra and trigonometry skills are
essential preparation for calculus.
1
, 1. LINES & SLOPE
• A line is straight, has infinitely many points, does not curve, and does not
end.
• To graph a specific line, two points are enough.
• A line can also be determined from one point plus its slope.
• Slope describes how a line rises or falls.
FORMULA
m = rise/run = Δy/Δx
For two points (x₁, y₁) and (x₂, y₂):
m = (y₂ - y₁) / (x₂ - x₁)
REMEMBER
Keep coordinates paired: if a point supplies x₁, the y-coordinate from that
same point must be y₁. Either point may be chosen as Point 1.
2
