Answer
[tex]y=\frac{1}{6}x+4[/tex]
Explanation
Given:
The given points are (6, 5) and (12, 6) where slope = 1/6
What to find:
The equation of the line.
Step-by-step solution:
The equation of a line of two points is given as
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]
Putting x₁ = 6, y₁ = 5, x₂ = 12, and y₂ = 6, the equation becomes
[tex]\begin{gathered} \frac{y-5}{x-6}=\frac{6-5}{12-6} \\ \\ \frac{y-5}{x-6}=\frac{1}{6} \\ \\ Cross\text{ }multiply \\ \\ 6(y-5)=x-6 \\ \\ 6y-30=x-6 \\ \\ Group\text{ }the\text{ }terms \\ \\ 6y=x-6+30 \\ \\ 6y=x+24 \\ \\ y=\frac{1}{6}x+4 \end{gathered}[/tex]
The equation of the line is:
[tex]y=\frac{1}{6}x+4[/tex]
