Slope
Calculate slope, equation, and angle of a line
How to use Slope
- 1Enter two point coordinates (x1, y1) and (x2, y2).
- 2Runs the calculator's tilt rate and y-axis cut-off.
- 3View the slope m, the cut-off b and the straight equation y = mx + b.
Slash
m = (y2 − y1) / (x2 − x1)；b = y1 − m × x1The slope measures the degree of a straight line tilt: if you remove it by moving it horizontally, that is, x changes y per unit.
The positive slope rises from left to right, the negative is down, zero is horizontal, and the undefined slope corresponds to the vertical straight line.
Slash m = (y2 − y1) / (x2 − x 1) indicating "how much is the vertical change when walking horizontally in 1 unit " . m > 0 right top tilt, m < 0 right bottom tilt, m = 0 level, ** vertical slope does not exist (sum 0)**. It's related to an oscillation of thorium, which is m = tan, which in turn is arctan(m). These two conversions are often used in engineering and game development.
There are also a few practical conclusions on the slope:** two straight lines paralleled the slash equal; and two line vertical slash multipliers -1** (i.e. negative penultimates, e.g. 2 and -1/2). This decision is much faster than the calculation of the angles. Also** percentage of slope ** angle**: 100% slope is 45° instead of 90°, 50% slope is about 26.6°. The "10% steep slope" on the road signs refers to an increase of 10 metres per 100 metres per advance, corresponding to about 5.7 degrees.
| Slope m | Angle | Percent slope | Typical scene |
|---|---|---|---|
| 0 | 0° | 0% | Horizontal |
| 0.0875 | 5° | 8.75% | Slow slope, wheelchair. |
| 0.176 | 10° | 17.6% | Get out of the garage. |
| 0.5 | 26.6° | 50% | The steep slope. |
| 1 | 45° | 100% | Straight-angle triangle |
| 1.732 | 60° | 173.2% | It's steep. |
| ∞ | 90° | — | Vertical (no slope) |
Slash against corresponding angles, common slopes
Frequently asked questions
If x is equal?
Lines are vertical and the slope is not defined (separate by zero).
What does that mean?
Moves one unit at each level and increases one unit vertically, i.e. 45° angle.
How do you get the equation?
When m is known, any point is added b = y = mx
What does the slope mean in the regression analysis?
In y = a + bx, b is the tilt rate, which represents the average change of y per unit added by x. For example, the regression equation "House price = 50 + 2 x area" with a slope of 2 which indicates an average increase of $20,000 for each square metre increase. A positive or negative sign of the slope reflects the direction and the size reflects the intensity of the impact, but note that the correlation is not equal to cause and effect.
What does it have to do with the gradient?
This is the specific case of a straight line (with the same number of points) in which the curve is tilted by the tangent at a point. In the curve, the slope varies from position to position, requiring the instantaneous rate of change to use a guide: function f(x) the index f'(x0) at x0 is the slope of the point tangent. So it's a special case of a "go" on a straight line, both of which are essentially "change rates."