Question

Find the equation for the

Answer 1

To find the equation of a line, we use the slope-intercept from formula shown below:

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

We just need 2 points from the line. They are:

`\begin{gathered} (x_1,y_1)=(5,-6) \\ \text{and} \\ (x_2,y_2)=(-3,-4) \end{gathered}`

Substituting, we get:

`\begin{gathered} y-y_1=(y_2-y_1)/(x_2-x_1)_{}(x-x_1) \\ y-(-6)=\frac{-4-(-6)_{}}{-3-5}(x-5)_{} \\ y+6=(-4+6)/(-8)(x-5) \\ y+6=(2)/(-8)(x-5) \\ y+6=-(1)/(4)(x-5) \\ y+6=-(1)/(4)x+(5)/(4) \\ y=-(1)/(4)x+(5)/(4)-6 \\ y=-(1)/(4)x-(19)/(4) \end{gathered}`