Question

Write an equation of the line passing through the points (3,-6) with the slope of -2/3

Answer 1

Step-by-step explanation:

The coordinate is given below as

`\begin{gathered} (x_1,y_1)=(3,-6) \\ slope=m=-(2)/(3) \end{gathered}`

Concept:

To calculate the equation of a line given slope and one point, we will use the formula below

`m=(y-y_1)/(x-x_1)`

By substituting the values, we will have

`\begin{gathered} m=(y-y_(1))/(x-x_(1)) \\ -(2)/(3)=(y-(-6))/(x-3) \\ -(2)/(3)=(y+6)/(x-3) \\ cross\text{ multpily, we will have} \\ 3(y+6)=-2(x-3) \\ 3y+18=-2x+6 \\ 3y=-2x+6-18 \\ 3y=-2x-12 \\ divide\text{ through by 3} \\ (3y)/(3)=-(2x)/(3)-(12)/(3) \\ y=-(2)/(3)x-4 \end{gathered}`

Hence,

The final answer is

`y=-(2)/(3)x-4`