Question

write an equation of the line that passes through a pair of points: (-2, -2), (5, -5)
a. $y = \frac{3}{7}x - \frac{20}{7}$ c. $y = -\frac{3}{7}x + \frac{7}{20}$
b. $y = -\frac{3}{7}x + \frac{20}{7}$ d. $y = -\frac{3}{7}x - \frac{20}{7}$
please select the best answer from the choices provided
a
b
c
d

Explanation:

Step1: Calculate the slope

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Given points \((-2, -2)\) and \((5, -5)\), we have \( x_1=-2,y_1 = - 2,x_2 = 5,y_2=-5 \).
So \( m=\frac{-5-(-2)}{5 - (-2)}=\frac{-5 + 2}{5+2}=\frac{-3}{7}=-\frac{3}{7} \).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \((-2,-2)\).
Substitute \( m =-\frac{3}{7},x_1=-2,y_1=-2 \) into the formula:
\( y-(-2)=-\frac{3}{7}(x - (-2)) \)
\( y + 2=-\frac{3}{7}(x + 2) \)
Expand the right - hand side: \( y+2=-\frac{3}{7}x-\frac{6}{7} \)
Subtract 2 from both sides. Since \( 2=\frac{14}{7} \), we have \( y=-\frac{3}{7}x-\frac{6}{7}-\frac{14}{7} \)
\( y=-\frac{3}{7}x-\frac{20}{7} \)

Answer:

D. \( y =-\frac{3}{7}x-\frac{20}{7} \)