Answer:
[tex]y+4=\frac{5}{3}(x+1)[/tex]
Step-by-step explanation:
The equation in the point-slope form of a line is written as
[tex]y-y_0 = m(x-x_0)[/tex] (1)
where
m is the slope of the line
[tex](x_0,y_0)[/tex] are the coordinates of a point on the line
In this problem, we hate two points belonging to the line:
[tex](x_0,y_0)=(-1,4)\\(x_1,y_1)=(2,1)[/tex]
Therefore we can find the slope with the following equation:
[tex]m=\frac{y_1-y_0}{x_1-x_0}=\frac{1-(-4)}{2-(-1)}=\frac{5}{3}[/tex]
And by substituting [tex]x_0 = -1\\y_0 = -4[/tex] into eq(1), we find
[tex]y+4=\frac{5}{3}(x+1)[/tex]
