what is the equation, in point - slope form, of the line that is parallel to the given line and passes…

what is the equation, in point - slope form, of the line that is parallel to the given line and passes through the point $(4,1)$?\n$y - 1=-2(x - 4)$\n$y - 1=-\frac{1}{2}(x - 4)$\n$y - 1=\frac{1}{2}(x - 4)$\n$y - 1=2(x - 4)$

what is the equation, in point - slope form, of the line that is parallel to the given line and passes through the point $(4,1)$?\n$y - 1=-2(x - 4)$\n$y - 1=-\frac{1}{2}(x - 4)$\n$y - 1=\frac{1}{2}(x - 4)$\n$y - 1=2(x - 4)$

Answer

Explanation:

Step1: Calculate the slope of the given line

Use the slope formula (m=\frac{y_2 - y_1}{x_2 - x_1}). Let ((x_1,y_1)=(-3,3)) and ((x_2,y_2)=(-2,1)). Then (m=\frac{1 - 3}{-2-(-3)}=\frac{-2}{1}=-2).

Step2: Determine the slope of the parallel line

Parallel lines have equal slopes. So the slope of the line we want is also (m=-2).

Step3: Use the point - slope form

The point - slope form is (y - y_0=m(x - x_0)), where ((x_0,y_0)=(4,1)) and (m=-2). Substituting gives (y - 1=-2(x - 4)).

Answer:

(y - 1=-2(x - 4)) (the first option)