write an equation in point - slope form for the line that passes through the given points. (1, - 3), (4, - 15)

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,-3)) and ((x_2,y_2)=(4,-15)). Then (m=\frac{-15-(-3)}{4 - 1}=\frac{-15 + 3}{3}=\frac{-12}{3}=-4).

Step2: Use the point - slope form

The point - slope form is (y - y_1=m(x - x_1)). Using the point ((1,-3)) and (m=-4), we get (y-(-3)=-4(x - 1)), which simplifies to (y + 3=-4(x - 1)). Using the point ((4,-15)) and (m=-4), we get (y-(-15)=-4(x - 4)), which simplifies to (y + 15=-4(x - 4)).

Answer:

(y + 3=-4(x - 1)) or (y + 15=-4(x - 4))