Respuesta :
We are asked to determine the equation of a line with a slope 1/3. The general form of a line equation is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" the y-intercept.
Now, we substitute the value of the slope:
[tex]y=\frac{1}{3}x+b[/tex]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:
[tex]8=\frac{1}{3}(6)+b[/tex]Solving the product on the right side we get:
[tex]8=2+b[/tex]Now, we subtract 2 from both sides:
[tex]\begin{gathered} 8-2=2-2+b \\ 6=b \end{gathered}[/tex]Now, we substitute the value in the equation of the line:
[tex]y=\frac{1}{3}x+6[/tex]And thus we get the equation of the line.
