Respuesta :
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.
