Question

What is the equation of the line shown here

Answer 1

`y=-2+(1)/(3)x`

Step-by-step explanation:

First, pick two points on the line: (6, 0) and (0, -2)

Next, using the two-point form of the equation of the line:

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

Substitute the points:

`\begin{gathered} (y-0)/(x-6)=(-2-0)/(0-6) \\ (y)/(x-6)=(-2)/(-6) \\ (y)/(x-6)=(1)/(3) \\ y=(1)/(3)(x-6) \end{gathered}`

We open the bracket:

`\begin{gathered} y=(1)/(3)x-2 \\ \implies y=-2+(1)/(3)x \end{gathered}`

The equation of the line is:

`y=-2+(1)/(3)x`