“line(in two dimensions)”的概念、定义、翻译、参考文献-科学参考

line(in two dimensions)

Mathematics

A line can be determined by two points on the line or by a single point with the direction of the line. In two dimensions the direction can be specified by the gradient. There are a number of related standard formats for lines in a plane.
Slope‐intercept form.
y = mx + c. The line has a gradient m and intercept at (0,c). For a vertical line the gradient is infinite and the equation is x = k (in this case there is no intercept on the y-axis).
Two‐point form.
The condition that the general point P(x,y) lies on the line through A(x₁,y₁) and B(x₂,y₂) is equivalent to requiring the gradient of AP = the gradient of $A B or \frac{y - y_{1}}{x - x_{1}} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} .$
Point‐slope form.
A line with gradient m passing through the point A(x₁,y₁) has equation y−y₁ = m(x−x₁).
Two‐intercept form.
When the equation is written as $\frac{x}{a} + \frac{y}{b} = 1$ the line cuts the axes at (a,0) and (0,b), making it very easy to draw the line.

单词	line(in two dimensions)
释义	line(in two dimensions) Mathematics A line can be determined by two points on the line or by a single point with the direction of the line. In two dimensions the direction can be specified by the gradient. There are a number of related standard formats for lines in a plane. Slope‐intercept form. y = mx + c. The line has a gradient m and intercept at (0,c). For a vertical line the gradient is infinite and the equation is x = k (in this case there is no intercept on the y-axis). Two‐point form. The condition that the general point P(x,y) lies on the line through A(x₁,y₁) and B(x₂,y₂) is equivalent to requiring the gradient of AP = the gradient of $A B or \frac{y - y_{1}}{x - x_{1}} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} .$ Point‐slope form. A line with gradient m passing through the point A(x₁,y₁) has equation y−y₁ = m(x−x₁). Two‐intercept form. When the equation is written as $\frac{x}{a} + \frac{y}{b} = 1$ the line cuts the axes at (a,0) and (0,b), making it very easy to draw the line.
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Slope‐intercept form.y = mx + c. The line has a gradient m and intercept at (0,c). For a vertical line the gradient is infinite and the equation is x = k (in this case there is no intercept on the y-axis).

Two‐point form.The condition that the general point P(x,y) lies on the line through A(x1,y1) and B(x2,y2) is equivalent to requiring the gradient of AP = the gradient of ABory−y1x−x1=y2−y1x2−x1.

Point‐slope form.A line with gradient m passing through the point A(x1,y1) has equation y−y1 = m(x−x1).

Two‐intercept form.When the equation is written as xa+yb=1 the line cuts the axes at (a,0) and (0,b), making it very easy to draw the line.

Slope‐intercept form.
y = mx + c. The line has a gradient m and intercept at (0,c). For a vertical line the gradient is infinite and the equation is x = k (in this case there is no intercept on the y-axis).

Two‐point form.
The condition that the general point P(x,y) lies on the line through A(x₁,y₁) and B(x₂,y₂) is equivalent to requiring the gradient of AP = the gradient of $A B or \frac{y - y_{1}}{x - x_{1}} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} .$

Point‐slope form.
A line with gradient m passing through the point A(x₁,y₁) has equation y−y₁ = m(x−x₁).

Two‐intercept form.
When the equation is written as $\frac{x}{a} + \frac{y}{b} = 1$ the line cuts the axes at (a,0) and (0,b), making it very easy to draw the line.