Question

Write the equation of the line that has a slope of 1/3 and passes through the point (6,8).

Answer 1

We are asked to determine the equation of a line with a slope 1/3. The general form of a line equation is:

`y=mx+b`

Where "m" is the slope and "b" the y-intercept.

Now, we substitute the value of the slope:

`y=(1)/(3)x+b`

Now, to determine the value of "b" we will use the fact that the line passes through the point (x, y) = (

6, 8). Now, we plug in these values in the equation:

`8=(1)/(3)(6)+b`

Solving the product on the right side we get:

`8=2+b`

Now, we subtract 2 from both sides:

`\begin{gathered} 8-2=2-2+b \\ 6=b \end{gathered}`

Now, we substitute the value in the equation of the line:

`y=(1)/(3)x+6`

And thus we get the equation of the line.