Question

What is an equation of the line that passes through (2,-3) and is perpendicular to y=x-5

Answer 1

y = -x - 1 is the equation of the line that passes through (2,-3) and is perpendicular to y = x - 5

Solution:

Given that we have to write the equation of the line that passes through (2,-3) and is perpendicular to y = 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

Given equation of line is:

y = x - 5

On comparing the above equation with eqn 1,

m = 1

We know that,

Product of slope of line and slope of line perpendicular to given line is equal to -1

Therefore,

$1 \times \text{ slope of line perpendicular to given line } = -1$

Slope of line perpendicular to given line = -1

Now we have to find the equation of line with slope -1 and passing through (2, -3)

Substitute m = -1 and (x, y) = (2, -3) in eqn 1

-3 = -1(2) + c

-3 = -2 + c

c = -3 + 2

c = -1

Substitute m = -1 and c = - 1 in eqn 1

y = -x - 1

Thus the equation of line is found