Question

goes through points (-2, -1) and (-3, 5)
y = -1/6x + 1
y = -6x - 13
y = 6x + 13
y = 1/6x - 1

Explanation:

Step1: Calculate the slope

The slope \( m \) between 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, \((x_1, y_1)=(-2, -1)\) and \((x_2, y_2)=(-3, 5)\). So, \( m=\frac{5 - (-1)}{-3 - (-2)}=\frac{6}{-1}=-6 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((-2, -1)\) and \( m = - 6 \), we have \( y-(-1)=-6(x - (-2)) \), which simplifies to \( y + 1=-6(x + 2) \).

Step3: Simplify the equation

Expand the right - hand side: \( y+1=-6x-12 \). Then, subtract 1 from both sides: \( y=-6x-13 \).

Answer:

\( y = - 6x-13 \) (corresponding to the blue option: \( y = - 6x - 13 \))