8) through: (-3, -2), perp. to y = x – 1A) y=-5x – 1 B) y=-4x – 5C) y=-x – 5 D) y=-5x – 4

Answer:The equation through (-3, -2) and perpendicular to y = x – 1 is y = -x -5 and option c is correct.Solution:Given, line equation is y = x – 1 ⇒ x – y – 1 = 0. And a point is (-3, -2) We have to find the line equation which is perpendicular to above given line and passing through the given point. Now, let us find the slope of the given line equation. [tex]\text { Slope }=\frac{-x \text { coefficient }}{y \text { coefficient }}=\frac{-1}{-1}=1[/tex]We know that, product of slopes of perpendicular lines is -1. So, 1 [tex]\times[/tex] slope of perpendicular line =  -1 slope of perpendicular line = -1 Now let us write point slope form for our required line. [tex]\mathrm{y}-\mathrm{y}_{1}=\mathrm{m}\left(\mathrm{x}-\mathrm{x}_{1}\right)[/tex] y – (-2) = -1(x – (-3)) y + 2 = -1(x + 3) y + 2 = -x – 3 x + y + 2 + 3 = 0 x + y + 5 = 0 y = -x -5 Hence the equation through (-3, -2) and perpendicular to y = x – 1 is y = -x -5 and option c is correct.