Question

find the equation of the line specified. the line passes through the points ( 7, -7) and ( 6, -5) a. y = -2x + 7 c. y = -2x - 7 b. y = 2x - 21 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 to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \( (7,-7) \) and \( m=-2 \). Substituting into the formula, we get \( y-(-7)=-2(x - 7) \), which simplifies to \( y + 7=-2x+14 \). Then, subtracting 7 from both sides, we have \( y=-2x + 7 \). We can also check by substituting the point \( (6,-5) \) into the equation \( y=-2x + 7 \). When \( x = 6 \), \( y=-2\times6 + 7=-12 + 7=-5 \), which matches the given point.

Answer:

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