Question

67. Extensions

Find the equation of the line that passes through the following points: (a, 0) and (c, d)

Answer 1

Equation of a line passing through two point (a, 0) and (c, d) is given by
`$y=(d)/(c-a) x-(a d)/(c-a)$`.

Explanation:

In the question, it is given that a line passes through (a, 0) and (c, d).

It is asked to write the equation of line.

To do so, first find the values which are given in the question and put it in the formula of the equation of line passing through two points.

Step 1 of 2

Passing point of the line is (a, 0).

Hence,
`$x_(1)=a$` and

`$$y_(1)=0 \text {. }$$`

Also, Passing point of the line is (c, d).

Hence,
`$x_(2)=c$` and

`$$y_(2)=d \text {. }$$`

Step 2 of 2

Substitute the above values in the formula of equation of line passing through two point given by
`$y-y_(1)=(y_(2)-y_(1))/(x_(2)-x_(1))\left(x-x_(1)\right)$`.

`y-y_(1)=(y_(2)-y_(1))/(x_(2)-x_(1))\left(x-x_(1)\right)$$\\ $y-0=(d-0)/(c-a)(x-a)$\begin{aligned}&y=(d)/(c-a)(x-a) \\&y=(d)/(c-a) x-(d a)/(c-a)\end{aligned}$$`

Hence,
`$y=(d)/(c-a) x-(d a)/(c-a)$`.