Question

write equation of the line containing (-1,-3) and (1,1)
y = 2x + 7
y = 2x - 1
y = -2x - 1
y = -2x + 1

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(-1,-3)$ and $(x_2,y_2)=(1,1)$. So $m=\frac{1-(-3)}{1-(-1)}=\frac{4}{2} = 2$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(1,1)$ and $m = 2$, we have $y - 1=2(x - 1)$.

Step3: Simplify the equation

Expand the right - hand side: $y - 1=2x-2$. Then add 1 to both sides to get $y=2x - 1$.

Answer:

B. $y = 2x-1$