Question

Write the equation of a line in slope-intercept form, that is perpendicular to -x + y = 1 and goes through (1, -5).

Answer 1

y = -x - 4 is the equation of a line in slope-intercept form, that is perpendicular to -x + y = 1 and goes through (1, -5)

Solution:

Given that we have to write the equation of a line in slope-intercept form, that is perpendicular to -x + y = 1 and goes through (1, -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:

-x + y = 1

Rearrange into slope intercept form

y = x + 1

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 (1, -5)

Substitute m = -1 and (x, y) = (1, -5) in eqn 1

-5 = -1(1) + c

c - 1 = -5

c = -5 + 1

c = -4

Substitute c = -4 and m = -1 in eqn 1

y = -x - 4

Thus the equation of line is found