Question

equation of line connecteing two given points

Answer 1

The equation of the line connecting two given points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$

(This is valid when $x_1 \neq x_2$. If $x_1 = x_2$, the equation is $x = x_1$.)

Answer 2

To find the equation of a line connecting two given points, say $(x_1, y_1)$ and $(x_2, y_2)$, follow these steps:

1. Calculate the slope (m) of the line. The slope is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ This formula is applicable when $x_1 \neq x_2$.

2. Use the point-slope form of the equation of a line. The equation of a line with slope $m$ passing through a point $(x_1, y_1)$ is: $y - y_1 = m(x - x_1)$

3. Substitute the expression for $m$ from step 1 into the point-slope form from step 2. This gives the two-point form of the equation of a line: $y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$ This equation can be rearranged into various standard forms (e.g., $Ax + By + C = 0$).

Special Case: If $x_1 = x_2$, the line is a vertical line. In this case, the slope is undefined, and the equation of the line is simply $x = x_1$ (or $x = x_2$).