which is an equation in point - slope form for the line that passes through the points $(-1,4)$ and…

which is an equation in point - slope form for the line that passes through the points $(-1,4)$ and $(3,-4)$?\n$y - 4 = 2(x + 3)$\n$y + 4 = -2(x - 3)$\n$y + 4 = 2(x - 3)$\n$y - 3 = -2(x + 4)$

which is an equation in point - slope form for the line that passes through the points $(-1,4)$ and $(3,-4)$?\n$y - 4 = 2(x + 3)$\n$y + 4 = -2(x - 3)$\n$y + 4 = 2(x - 3)$\n$y - 3 = -2(x + 4)$

Answer

Explanation:

Step1: Calculate the slope

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). Let ((x_1,y_1)=(-1,4)) and ((x_2,y_2)=(3,-4)). Then (m=\frac{-4 - 4}{3-(-1)}=\frac{-8}{4}=-2).

Step2: Use the point - slope form

The point - slope form is (y - y_0=m(x - x_0)). Using the point ((x_0,y_0)=(3,-4)) and (m = - 2), we substitute into the formula: (y-(-4)=-2(x - 3)), which simplifies to (y + 4=-2(x - 3)).

Answer:

(y + 4=-2(x - 3)) (the second option)