Point slope form — lesson. Mathematics State Board, Class 10.

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Let us find the equation of the straight line passing through the point

$A(x_1,y_1)$ and having slope

$m$ .

Let

$P(x,y)$ be another point other than

$A$ . Then, the slope of the line joining the points

$A$ and

$P$ is given by:

$m = tan \theta = \frac{y - y_1}{x - x_1}$

$(x - x_1)m = y - y_1$

Therefore, the equation of the straight line is

$(x - x_1)m = y - y_1$ [Point slope form]

Example:

Find the equation of the line passing through the points

$(2,-3)$ , and the slope is

$\frac{1}{5}$ .

Solution:

Given that

$(x_1,y_1) = (2,-3)$ and

$m = \frac{1}{5}$

Substituting the known values in the formula,

$(x - x_1)m = y - y_1$ , we get:

$(x - 2)\frac{1}{5} = y + 3$

$x - 2 = 5(y + 3)$

$x - 2 = 5y + 15$

$x - 5y - 15 - 2 = 0$

$x - 5y - 17 = 0$

Therefore, the equation of the straight line is

$x - 5y - 17 = 0$

Did you find an error?

5. Point slope form