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Annette [7]
3 years ago
9

Consider the line y = 7x-9.

Mathematics
1 answer:
KatRina [158]3 years ago
8 0

y = \frac{-1}{7}x -\frac{8}{7} is the equation of the line that is perpendicular to this line and passes through the point (6, -2)

y = 7x - 44 equation of the line that is parallel to this line and passes through the point (6, -2)

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

<em><u>Given that line is:</u></em>

y = 7x - 9

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

y = mx + b ------ eqn 1

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

On comparing eqn 1 with y = 7x - 9 we get,

m = 7

<h3><u>Find the equation of the line that is perpendicular to this line and passes through the point (6, -2)</u></h3>

We know that,

Product of slope of a line and slope of line perpendicular to given is always -1

Therefore,

7 \times \text{ slope of line perpendicular to it } = -1\\\\\text{ slope of line perpendicular to it } = \frac{-1}{7}

Now find the equation of line:

\text{ Substitute } m = \frac{-1}{7} \text{ and } (x, y) = (6, -2) \text{ in eqn 1}

-2 = \frac{-1}{7} \times 6 + b\\\\-2 = \frac{-6}{7} + b\\\\b = -2+\frac{6}{7}\\\\b = \frac{-14+6}{7}\\\\b = \frac{-8}{7}

\text{Substitute } m = \frac{-1}{7} \text{ and } b = \frac{-8}{7} \text{ in eqn 1}\\\\y = \frac{-1}{7}x -\frac{8}{7}

Thus the equation of line perpendicular to given line is found

<h3><u>Find the equation of the line that is parallel to this line and passes through the point (6, -2)</u></h3>

Slopes of parallel lines are equal

Therefore,  m = 7

<em><u>Substitute m = 7 and (x, y) = (6, -2) in eqn 1</u></em>

-2 = 7(6) + b

-2 = 42 + b

b = -44

<em><u>Substitute m = 7 and b = -44 in eqn 1</u></em>

y = 7x - 44

Thus equation of line parallel to given line is found

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