Respuesta :
The equation of line passing through (2, -2) and parallel to [tex]y = \frac{-1}{2}x+5[/tex] is [tex]y = \frac{-x}{2}-1[/tex]
Solution:
We have to find the equation of line passing through (2, -2) and parallel to [tex]y = \frac{-1}{2}x+5[/tex]
The equation of line in slope intercept form is given as:
y = mx + c ------- eqn 1
Where "m" is the slope of line and "c" is the y-intercept
On comparing the given equation of line [tex]y = \frac{-1}{2}x+5[/tex] with eqn 1,
[tex]m = \frac{-1}{2}[/tex]
We know that slope of a line and slope of line parallel to it is always equal
Therefore, slope of line parallel to given line is also [tex]m = \frac{-1}{2}[/tex]
Substitute (x, y) = (2, -2) and [tex]m = \frac{-1}{2}[/tex] in eqn 1
[tex]-2=\frac{-1}{2}(2)+c\\\\-2 = -1+c\\\\c = -2+1\\\\c = -1[/tex]
Substitute c = -1 and [tex]m = \frac{-1}{2}[/tex] in eqn 1
[tex]y = \frac{-1}{2}x -1\\\\y = \frac{-x}{2}-1[/tex]
Thus equation of line parallel to given line is found
