Question

find the equation of the line specified. the line passes through the points ( 7, -7) and ( 6, -5) a. y = -2x + 7 b. y = 2x - 21 c. y = -2x - 7 d. y = 2x - 7 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 \((7, -7)\) and \((6, -5)\), we have \( x_1 = 7,y_1=-7,x_2 = 6,y_2=-5 \). So \( m=\frac{-5-(-7)}{6 - 7}=\frac{-5 + 7}{-1}=\frac{2}{-1}=-2 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \((7,-7)\) (we could also use \((6,-5)\)). Substitute \( m=-2,x_1 = 7,y_1=-7 \) into the formula: \( y-(-7)=-2(x - 7) \). Simplify this: \( y + 7=-2x+14 \). Then subtract 7 from both sides: \( y=-2x + 14-7=-2x + 7 \).

Answer:

A. \( y=-2x + 7 \)