Two point form — lesson. Mathematics State Board, Class 10.

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Let

$A$ and

$B$ be two distinct points whose coordinates are

$(x_1,y_1)$ and

$(x_2,y_2)$ , respectively. The slope of the straight line passing through the points

$A$ and

$B$ is

$m = \frac{y_2 - y_1}{x_2 - x_1}$ where (

$x_1 \neq x_2$ ).

Substitute the value of

$m$ in point slope form, we get:

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

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

Therefore, the equation of the line in two point form is

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

Example:

Find the equation of the straight line passing through the points

$(-1,6)$ and

$(2,5)$ .

Solution:

Here,

$(x_1,y_1) = (-1,6)$

$(x_2,y_2) = (2,5)$

Substituting the known values in the formula

$\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}$ , we get:

$\frac{y - 6}{5 - 6} = \frac{x + 1}{2 - 6}$

$\frac{y - 6}{-1} = \frac{x + 1}{-4}$

$-4(y - 6) = -1(x + 1)$

$-4y + 24 = -x - 1$

$x - 4y + 25 = 0$

Therefore, the equation of the straight line passing through the points

$(-1,6)$ and

$(2,5)$ is

$x - 4y + 25 = 0$ .

Did you find an error?

6. Two point form