Question

What is the equation of the line that passes through the point (-3,7) 1/3?

Answer 1

This a point-slope equation of a line problem.

The point-slope form of an equation of a line is given by the equation:

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{where:} \\ (x_1,y_1)\text{ is one point on the line} \\ m\text{ is the slope} \end{gathered}`

From the provided information, we have:

`\begin{gathered} m=(1)/(3) \\ one\text{ point (-3,7)} \\ x_1=-3;y_1=7 \end{gathered}`

Thus, the equation of the line is:

`\begin{gathered} y-7=(1)/(3)(x-(-3)) \\ y-7=(1)/(3)(x+3) \\ \text{cross}-\text{multiply} \\ 3(y-7)=x+3 \\ 3y-21=x+3 \\ 3y=x+3+21 \\ 3y=x+24 \\ y=(x+24)/(3) \\ y=(x)/(3)+(24)/(3) \\ y=(x)/(3)+8 \end{gathered}`

Hence, the equation of the line is:

`y=(x)/(3)+8`