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Leto [7]
3 years ago
13

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

Mathematics
1 answer:
allochka39001 [22]3 years ago
5 0

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)

<em><u>Solution:</u></em>

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)

<em><u>The equation of line in slope intercept form is given as: </u></em>

y = mx + c ------ eqn 1

Where, "m" is the slope of line and "c" is the y intercept

<em><u> Given equation of line is:</u></em>

-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

<em><u>Now we have to find the equation of line with slope -1 and passing through (1, -5)</u></em>

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

-5 = -1(1) + c

c - 1 = -5

c = -5 + 1

c = -4

<em><u>Substitute c = -4 and m = -1 in eqn 1</u></em>

y = -x - 4

Thus the equation of line is found

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