Question

write an equation of the line that passes through a pair of points: (-3, 1), (-2, -5)
a. y = 6x - 17
b. y = -6x - 17
c. y = -6x + 17
d. y = -6x + \frac{1}{17}
please select the best answer from the choices provided
a
b
c
d

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For the points \((-3, 1)\) and \((-2, -5)\), we have \( x_1=-3, y_1 = 1, x_2=-2, y_2=-5 \). So \( m=\frac{-5 - 1}{-2-(-3)}=\frac{-6}{1}=-6 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((-3, 1)\) and \( m=-6 \), we get \( y - 1=-6(x + 3) \).

Step3: Simplify the equation

Expand the right - hand side: \( y-1=-6x-18 \). Then add 1 to both sides: \( y=-6x-18 + 1=-6x-17 \).

Answer:

B. \( y=-6x - 17 \)