Question

Write the equation of each line with the given points and slope. Complete parts (a) through (d) below.

Answer 1

`y=(1)/(6)x+4`

Step-by-step 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

`\begin{gathered} (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \\ \end{gathered}`

Putting x₁ = 6, y₁ = 5, x₂ = 12, and y₂ = 6, the equation becomes

`\begin{gathered} (y-5)/(x-6)=(6-5)/(12-6) \\ \\ (y-5)/(x-6)=(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=(1)/(6)x+4 \end{gathered}`

The equation of the line is:

`y=(1)/(6)x+4`