Question

What is the point -slope form of a line passing through the point(-3,4) and having the slope 5/6.

Answer 1

Given:

The point given is

`(x_1,y_1)=(-3,4)`

and the slope is

`m=(5)/(6)`

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

`(x_(1,)y_1)`

and having slope

`m`

is given by,

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

Thus, by substituting the values, the point-slope form of a line passing through the given point is,

`\begin{gathered} y-y_1=m(x-x_1) \\ y-4=(5)/(6)(x-(-3)) \\ 6(y-4)=5(x+3) \\ 6y-24=5x+15 \\ 6y=5x+15+24 \\ 6y=5x+39 \\ y=(5)/(6)x+(39)/(6) \\ y=(5)/(6)x+(13)/(2) \end{gathered}`

Final Answer:

The point-slope form of a line passing through the given point is,

`y=(5)/(6)x+(13)/(2)`