Question

On a graph paper, draw a line parallel to the x or y axis. Write coordinates of any four points on the line. Write how the equation of the line can be obtained using the given points.

Answer 1

Hint: To obtain the equation of line from the position of points lying on the line, we can use the formula-
$\mathrm{y}-{\mathrm{y}}_1={\displaystyle \frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}}(\mathrm{x}-{\mathrm{x}}_1)$

Complete step-by-step answer:
The line and four points are given as follows-
 

Let us take the line parallel to y axis with four points on the line as A(5,1) , B(5,2) ,C(5,5) and D(5,6)
To find the equation of line, only two points are required. So, we can choose any two points randomly to find the equation of line. Using points A and B,

$$\begin{gathered} \mathrm{y}-1={\displaystyle \frac{2-1}{5-5}}(\mathrm{x}-5) \\ 0(\mathrm{y}-1)=\mathrm{x}-5 \\ \mathrm{x}=5 \end{gathered}$$
This is the equation of the line. The other two points C(5,5) and D(5,6.5) also satisfy the equation of the line.

Note: If we assume any other points like C and D, we will get the same equation as in the answer. Students should take care that they draw the key and mark the axes correctly on the graph sheet.