Question

Through (2,-2) parallel to y= -1/2x+5

Answer 1

The equation of line passing through (2, -2) and parallel to
`y = (-1)/(2)x+5` is
`y = (-x)/(2)-1`

Solution:

We have to find the equation of line passing through (2, -2) and parallel to
`y = (-1)/(2)x+5`

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
`y = (-1)/(2)x+5` with eqn 1,

`m = (-1)/(2)`

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
`m = (-1)/(2)`

Substitute (x, y) = (2, -2) and
`m = (-1)/(2)` in eqn 1

`-2=(-1)/(2)(2)+c\\\\-2 = -1+c\\\\c = -2+1\\\\c = -1`

Substitute c = -1 and
`m = (-1)/(2)` in eqn 1

`y = (-1)/(2)x -1\\\\y = (-x)/(2)-1`

Thus equation of line parallel to given line is found