which equation represents the line that passes through the points (4, 1) and (0, 3)?\na $y +…

which equation represents the line that passes through the points (4, 1) and (0, 3)?\na $y + 1=-\frac{1}{2}(x + 4)$\nb $y - 1=-\frac{1}{2}(x - 4)$\nc $y - 4=-\frac{1}{2}(x - 1)$\nd $y + 4=-\frac{1}{2}(x + 1)$

which equation represents the line that passes through the points (4, 1) and (0, 3)?\na $y + 1=-\frac{1}{2}(x + 4)$\nb $y - 1=-\frac{1}{2}(x - 4)$\nc $y - 4=-\frac{1}{2}(x - 1)$\nd $y + 4=-\frac{1}{2}(x + 1)$

Answer

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(4,1)$ and $(x_2,y_2)=(0,3)$. Then $m=\frac{3 - 1}{0 - 4}=\frac{2}{-4}=-\frac{1}{2}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(4,1)$ and $m =-\frac{1}{2}$, we get $y - 1=-\frac{1}{2}(x - 4)$.

Answer:

B. $y - 1=-\frac{1}{2}(x - 4)$