Straight Lines — Class 11 CBSE Mathematics revision notes
A 4-page visual revision sheet for Straight Lines, written for Class 11 CBSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Straight Lines in one look
one slope, four forms, and the general equation that ties them together
Angle of inclination and slope
- the angle of inclination θ of a line is measured from the positive x-axis, counter-clockwise, with 0°≤θ<180°
- slope m=tanθ, defined for every θ except 90°
- θ=0° gives a horizontal line, m=0; θ=90° gives a vertical line, where slope is undefined
- a line rising left to right has 0°<θ<90°, so m>0; a line falling left to right has 90°<θ<180°, so m<0
Slope from two points, and the two big conditions
- slope through (x_1,y_1) and (x_2,y_2), x_1≠ x_2
m=y_2-y_1/x_2-x_1 - two lines are parallel exactly when
m_1=m_2 - two lines are perpendicular exactly when
m_1m_2=-1
Four special lines
- Horizontal line: θ=0°, m=0, equation y=k for some constant k
- Vertical line: θ=90°, slope undefined, equation x=k for some constant k
- Through the origin: y-intercept is 0, equation reduces to y=mx
- At 45° to the x-axis: θ=45°, so m=tan45°=1
Point-slope and two-point forms
- line through (x_1,y_1) with slope m
y-y_1=m(x-x_1) - line through (x_1,y_1) and (x_2,y_2), x_1≠ x_2
y-y_1=y_2-y_1/x_2-x_1(x-x_1)
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Straight Lines sheet covers
- Angle of inclination and slope
- Slope from two points, and the two big conditions
- slope through (x_1,y_1) and (x_2,y_2), x_1≠ x_2
- two lines are parallel exactly when
- two lines are perpendicular exactly when
- Four special lines
- Horizontal line
- Vertical line
- Through the origin
- At 45° to the x-axis
- Point-slope and two-point forms
- line through (x_1,y_1) with slope m
- line through (x_1,y_1) and (x_2,y_2), x_1≠ x_2
- Slope-intercept, intercept and normal forms
- slope m, y-intercept c
- x-intercept a, y-intercept b, both nonzero
- perpendicular distance p from the origin, at angle ω to the x-axis, p>0
- Which form fits what's given
- The general equation
- Angle between two lines
- slope form, whenever 1+m_1m_2≠0
- general form, perpendicular exactly when
- Worked: equation of a line, then its distance from the origin
- Distance formulas
- perpendicular distance of (x_1,y_1) from Ax+By+C=0
- distance between two parallel lines Ax+By+C_1=0 and Ax+By+C_2=0
- Symbols
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Straight Lines the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.