Question

(1 point)
\\(\bigcirc\\) \\(y = -\frac{7}{6}x - \frac{23}{3}\\)
\\(\bigcirc\\) \\(y = \frac{6}{7}x + \frac{46}{7}\\)
\\(\bigcirc\\) \\(y = -\frac{6}{7}x - \frac{46}{7}\\)
\\(\bigcirc\\) \\(y = -\frac{6}{7}x - 7\\)

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \((-10, 2)\) and \((4, -10)\):
\( m=\frac{-10 - 2}{4 - (-10)}=\frac{-12}{14}=-\frac{6}{7} \)

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((-10, 2)\) and \( m =-\frac{6}{7} \):
\( y - 2=-\frac{6}{7}(x + 10) \)
Expand the right - hand side:
\( y-2=-\frac{6}{7}x-\frac{60}{7} \)
Add 2 to both sides. Since \( 2=\frac{14}{7} \):
\( y=-\frac{6}{7}x-\frac{60}{7}+\frac{14}{7} \)
\( y =-\frac{6}{7}x-\frac{46}{7} \)

Answer:

\( y =-\frac{6}{7}x-\frac{46}{7} \) (the third option)