Question

How can I get to know the equation of a straight line when I have the two points?

Answer 1

`y=5x-6`

Step-by-step explanation

Let the two points be (2, 4) and (3, 9).

The general form of the equation of a straight line is given by:

`y=mx+b`

where m = slope

b = y-intercept

First, we have to find the slope of the line using the formula:

`m=(y_2-y_1)/(x_2-x_1)`

where (x1, y1) and (x2, y2) are the two points that the line passes through

Therefore, the slope of the line is:

`\begin{gathered} m=(9-4)/(3-2)=(5)/(1) \\ m=5 \end{gathered}`

Now, we find the equation of the line using the point-slope method:

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

Therefore, the equation of the line is:

`\begin{gathered} y-4=5(x-2) \\ y-4=5x-10 \\ y=5x-10+4 \\ y=5x-6 \end{gathered}`