Question

determine the equation of the line that passes through the given points. (if you have a graphing calculator, you can use the table feature to confirm that the coordinates of both points satisfy your equation.) (-5, 10) and (5, -10) a. $y = 2x - 10$ b. $y = 2x$ c. $y = -2x + 20$ d. $y = -2x$ 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 \((-5, 10)\) and \((5, -10)\), we have \( x_1=-5,y_1 = 10,x_2 = 5,y_2=-10 \). So \( m=\frac{-10 - 10}{5-(-5)}=\frac{-20}{10}=-2 \).

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 \((-5,10)\) and \( m=-2 \). Substitute into the formula: \( y - 10=-2(x+5) \).

Step3: Simplify the equation

Expand the right - hand side: \( y - 10=-2x-10 \). Add 10 to both sides of the equation: \( y=-2x \). We can also check by substituting the two points into the equation \( y = - 2x \). For \((-5,10)\): when \( x=-5 \), \( y=-2\times(-5)=10 \), which matches. For \((5,-10)\): when \( x = 5 \), \( y=-2\times5=-10 \), which also matches.

Answer:

D. \( y = -2x \)