Option C:
[tex]y+6=\frac{3}{5} (x-4)[/tex]
Solution:
Given point (4, –6) and slope, [tex]m=\frac{3}{5}[/tex]
Formula for equation of a straight line when passing through the point [tex](x_1, y_1)[/tex] and slope m is [tex]y-y_1=m(x-x_1)[/tex]
Here, [tex]x_1=4, y_1=-6, m=\frac{3}{5}[/tex]
Substitute these in the above formula, we get
⇒ [tex]y-(-6)=\frac{3}{5} (x-4)[/tex]
⇒ [tex]y+6=\frac{3}{5} (x-4)[/tex]
Hence, [tex]y+6=\frac{3}{5} (x-4)[/tex] is the equation in point-slope form.
