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Class 9 Coordinate Geometry (Advanced): cheat sheet
CBSE Mathematics. Slope measures how steep a line is. A straight line can be written in general, slope-intercept or intercept form, depending on what is known.
Key ideas
- Reflect in the x-axis: y changes sign; in the y-axis: x changes sign; in the origin: both change sign.
- The distance of (a, b) from the x-axis is |b| and from the y-axis is |a|.
- Positive slope rises from left to right; negative slope falls; a horizontal line has slope 0; a vertical line has no slope.
- Three points are on one line exactly when the slopes between them are equal.
- Find intercepts by putting y = 0 (x-intercept) or x = 0 (y-intercept).
- The signs of the two intercepts tell you which one quadrant a line never enters.
Remember
| Slope through two points | m = (y₂ − y₁) ÷ (x₂ − x₁) |
| Parallel and perpendicular | m₁ = m₂; m₁m₂ = −1 |
| General form Ax + By + C = 0 | slope −A/B; x-intercept −C/A; y-intercept −C/B |
| Slope-intercept form | y = mx + c (c is the y-intercept) |
| Intercept form | x/a + y/b = 1 (cuts the axes at (a, 0) and (0, b)) |
| Triangle with the axes | area = ½ × |a| × |b| |
Watch out
- Subtracting the coordinates in different orders on the top and the bottom of the slope formula.
- Taking the perpendicular slope as −m instead of −1/m.
- Forgetting that a distance from an axis is never negative.
Worked example
For the line −5x + 4y + 10 = 0, find the slope and both intercepts, and name the quadrant it never passes through.
Working: slope = −A/B; x-intercept = −C/A; y-intercept = −C/B; a line through (2, 0) and (0, −5/2) passes through the other three quadrants
Answer: slope 5/4, x-intercept 2, y-intercept −5/2; it misses quadrant II
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