CBSE Class 11 · Mathematics
Straight Lines
Official NCERT chapter from Mathematics (book code kemh1). ExamMaster notes are original teaching at CBSE Class 11 depth.
This lesson follows the official chapter “Straight Lines” in Mathematics. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.
- CBSE Class 11
- Medium level
- 8 concepts
1Slope of a Line
Slope m is rise over run: (y2−y1)/(x2−x1) when x2≠x1. From (1, 2) to (4, 8), m=2. A vertical line has no this m (undefined as taught). Parallel lines share m; perpendiculars multiply to −1 (as taught, neither vertical).
Using run over rise is the flip-steal.
Figure. Slope is rise over run on the drawn triangle. The vertical span is half the horizontal span on screen, so m = 2/4 = 1/2. The triangle is to scale for that ratio.
How it works
- Subtract ys over subtract xsThe slope.
- Name parallel (same m) or perpendicular (m1 m2=−1)The compare.
- Refuse a vertical as “m=∞ in the arithmetic” without the lesson’s wordUndefined.
2Various Forms of the Equation of a Line
Forms of a line: slope-intercept y=mx+c; point-slope y−y1=m(x−x1); two-point; intercept x/a+y/b=1 as taught. One line, many writings. y=2x+1 and 2x−y+1=0 are the same line. A form is a writing, not a different line.
Treating two forms as two lines because they look busy is a miss.
Figure. Intercept form names the cuts: A is (a, 0) on the x-axis and B is (0, b) on the y-axis. The same line is x/a + y/b = 1. The intercepts are labelled, not to a numeric scale.
How it works
- Pick the form the given fitsm and a point, or two points…
- Write it, then rearrange if askedThe equation.
- Check a known point sits on itSame line.
Through (1, 2), m=2
Write the point-slope form, then y=mx+c.
- Point-slopey−2=2(x−1)
- Expandy=2x
- Waity−2=2x−2 → y=2x — c=0
Pro tip. Same line; (1,2) and m=2 force c=0.
3Distance of a Point From a Line
Distance from (x0,y0) to ax+by+c=0 is |ax0+by0+c|/√(a²+b²) as taught. From (0,0) to x+2y−4=0 is 4/√5. Distance is a length, not the intercept.
Dropping the absolute value can print a negative length.
Figure. Distance from P to L is the perpendicular PN, not a slant walk along the line. L is drawn horizontal so the right angle at N is a true square, independent of aspect.
How it works
- Write the line as ax+by+c=0The prepare.
- Plug the point; take | | over the rootThe distance.
- Keep the unit if the grid has oneA length.
4A definition is a test you can run
Line / slope / distance is a test: m, an equation, or the point-to-line length. If you only say “straight”, you have a heading.
A ruler-photo is not the test.
Figure. Parallel is a test you can run: a transversal that makes a matching pair 70° and 70° earns the parallel mark. Looking tidy is not the test.
How it works
- Name two points or a,b,cThe object.
- Give m or the form or the distanceThe test.
- Then the word has contentThe definition ran.
5Name the given before the unknown
The given are two points or m and a point. The unknown is the equation or the distance. Copy (1,2) before you use (2,1).
Using rise 8 and run 4 because those were the coordinates, not the differences, is a silent given.
Figure. Ink the given points first. P and Q are known; the slope is the unknown you ask after those marks exist.
How it works
- Copy the points or mThe given.
- Name the equation or the lengthThe unknown.
- Then subtract or plugGiven first.
6One worked case is enough at this class
One line is enough. A page of the same m=2 clone does not add a new intercept form.
Ten twins of y=2x are still one idea.
Figure. One numerical case: from (1, 2) to (7, 5) the run is 6 and the rise is 3, so m = 3/6 = 1/2. The triangle is to scale for that half-slope.
How it works
- Write one equation or one distanceThe case.
- A second only as a checkOptional.
- StopThis class.
7A miss: swapping the school name for the picture
A road-photo is a setting. The maths is m and an equation. A hill-feel is not m=2.
A railway still is not ax+by+c=0.
Figure. The chapter title is a name. The picture is the rise-over-run triangle. Swapping the school name for the drawing leaves you with a word and no slope.
How it works
- Keep the road as a storyA setting.
- Write two points or mThe maths.
- Then the formDo not swap.
8Check by the opposite action or the opposite test
Check an equation by plugging a given point; check distance by a second form of the same line. (1,2) must sit on y=2x.
A sketch that “looks 2” is not the opposite test.
Figure. Swap the ends and the slope must stay 1/2. A to B and B to A are the same line; a check that disagrees means the rise or run was signed wrong.
How it works
- State y=2x or 4/√5The claim.
- Substitute or rearrange and recomputeThe check.
- Mend if they disagreeHonest.
Slope from (1, 2) to (4, 8) is
- 2
- 3
- 6/3 as 1
(8−2)/(4−1)=2.
Notes
- The official chapter title is “Straight Lines”. Teach the school test for that title, not a contest shortcut.
- If a step needs a later class, stop. The next official chapter will pick it up.
Formulas
- m=(y2−y1)/(x2−x1)
- y−y1=m(x−x1)
- dist=|ax0+by0+c|/√(a²+b²)
Recap
Hold these pegs from the official chapter “Straight Lines”. The wording is ExamMaster’s teaching, not a textbook recap.
- Slope of a Line
- Slope m is rise over run: (y2−y1)/(x2−x1) when x2≠x1.
- Various Forms of the Equation of a Line
- Forms of a line: slope-intercept y=mx+c; point-slope y−y1=m(x−x1); two-point; intercept x/a+y/b=1 as taught.
- Distance of a Point From a Line
- Distance from (x0,y0) to ax+by+c=0 is |ax0+by0+c|/√(a²+b²) as taught.
- A definition is a test you can run
- Line / slope / distance is a test: m, an equation, or the point-to-line length.
- Name the given before the unknown
- The given are two points or m and a point.
- One worked case is enough at this class
- One line is enough. A page of the same m=2 clone does not add a new intercept form.
Practise Straight Lines
Reading is free and needs no account. Practice, mocks and progress live in the app.
- A 4-question practice set that ends the chapter
- 1 quick check with worked explanations
- Timed mocks scored with the real marking scheme
- Readiness tracked per topic, kept on your device