Question

Which equation is in point-slope form and depicts the equation of this line?

Answer 1

`y+4=(5)/(3)(x+1)`

Explanation:

The equation in the point-slope form of a line is written as

`y-y_0 = m(x-x_0)` (1)

where

m is the slope of the line

`(x_0,y_0)` are the coordinates of a point on the line

In this problem, we hate two points belonging to the line:

`(x_0,y_0)=(-1,4)\\(x_1,y_1)=(2,1)`

Therefore we can find the slope with the following equation:

`m=(y_1-y_0)/(x_1-x_0)=(1-(-4))/(2-(-1))=(5)/(3)`

And by substituting
`x_0 = -1\\y_0 = -4` into eq(1), we find

`y+4=(5)/(3)(x+1)`