Question

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

Answer 1

The equation of line passing through (2, -2) and parallel to $y = \frac{-1}{2}x+5$ is $y = \frac{-x}{2}-1$

Solution:

We have to find the equation of line passing through (2, -2) and parallel to $y = \frac{-1}{2}x+5$

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 $y = \frac{-1}{2}x+5$ with eqn 1,

$m = \frac{-1}{2}$

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 $m = \frac{-1}{2}$

Substitute (x, y) = (2, -2) and $m = \frac{-1}{2}$ in eqn 1

$-2=\frac{-1}{2}(2)+c\\\\-2 = -1+c\\\\c = -2+1\\\\c = -1$

Substitute c = -1 and $m = \frac{-1}{2}$ in eqn 1

$y = \frac{-1}{2}x -1\\\\y = \frac{-x}{2}-1$

Thus equation of line parallel to given line is found