Question

The equation of the line through (2, 3) and (6, 11).is y = mx - 1.

Answer 1

Given:

There are given the points:

`(2,3),and,(6,11)`

Step-by-step explanation:

According to the question:

We need to find the equation:

So,

To find the equation, first, we need to find the slope of the line:

So,

From the formula of slope:

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

Then,

`\begin{gathered} m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ m=(11-3)/(6-2) \\ m=(8)/(4) \\ m=2 \end{gathered}`

Now,

From the formula to find the equation of line:

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

Then,

`\begin{gathered} y-y_(1)=m(x-x_(1)) \\ y-3=2(x-2) \\ y-3=2x-4 \\ y=2x-4+3 \\ y=2x-1 \end{gathered}`

Final answer:;

Hence, the equation of the line is shown below:

`y=2x-1`