Question

Find the equation of a line through t
he points (8,1) (10,11) on a graph

Answer 1

Given: A straight line passes through the points (8, 1) and (10, 11).

To find: The equation of the line

Solution:

We will use the concept of two point form to find the required equation of line.

Whenever we are given two points through which the given line passes, then the equation of the line is given by:

• $\boxed{ \sf (y - y_1) =\left( \dfrac{y_2-y_1}{x_2-x_1}\right) (x-x_1)}$

Let's assume that:

• (x1, y1) = (8, 1)
• (x2, y2) = (10, 11)

Therefore the required equation of the line is:

$\sf \implies (y - y_1) =\left( \dfrac{y_2-y_1}{x_2-x_1}\right) (x-x_1)$

$\sf \implies (y - 8) =\left( \dfrac{11 - 1}{10 - 8}\right) (x - 8)$

$\sf \implies (y - 8) =\left( \dfrac{10}{2}\right) (x - 8)$

$\sf \implies (y - 8) =\left(5\right) (x - 8)$

$\sf \implies y - 8 =5x - 40$

$\sf \implies 5x - y - 40 + 8 = 0$

$\boxed{ \purple{\sf \implies 5x - y -32 = 0}}$

This is the required equation of straight line.

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