Given:
The point given is
[tex](x_1,y_1)=(-3,4)[/tex]and the slope is
[tex]m=\frac{5}{6}[/tex]Required:
Point-slope form of a line passing through given point.
Answer:
Here, we use the point-slope form of a line passing through the point
[tex](x_{1,}y_1)[/tex]and having slope
[tex]m[/tex]is given by,
[tex]y-y_1=m(x-x_1)[/tex]Thus, by substituting the values, the point-slope form of a line passing through the given point is,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-4=\frac{5}{6}(x-(-3)) \\ 6(y-4)=5(x+3) \\ 6y-24=5x+15 \\ 6y=5x+15+24 \\ 6y=5x+39 \\ y=\frac{5}{6}x+\frac{39}{6} \\ y=\frac{5}{6}x+\frac{13}{2} \end{gathered}[/tex]Final Answer:
The point-slope form of a line passing through the given point is,
[tex]y=\frac{5}{6}x+\frac{13}{2}[/tex]
