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Write the equation of the line passes through the point (10, 2) and is perpendicular to the line: y=-5x+7

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User Lit
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1 Answer

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Answer:

Perpendicular line: y = ⅕x + 0 or y = ⅕x

Explanation:

Given the point, (10, 2), and the linear equation, y = -5x + 7:

In order to find the equation of the perpendicular line that passes through (10, 2), we must first determine the definition of perpendicular lines.

Definition:

Perpendicular lines have negative reciprocal slopes ⇒ this means that when you take and multiply the slopes of both lines, it results in a product of -1.

  • In other words, since the slope of the given line, y = -5x + 7 is m = -5, then it means that the slope of the other line must be m₂ = ⅕ because:

m₁ × m₂ = -1

-5 × ⅕ = -1

Solution:

Now that we have the slope of the other line, m₂ = ⅕, and the given point, (10, 2), substitute these values into the slope-intercept form to solve for the y-intercept, b :

y = mx + b

2 = ⅕(10) + b

2 = 2 + b

Subtract 2 from both sides:

2 -2 = 2 -2 + b

0 = b

Hence, the y-intercept is b = 0.

Equation:

The linear equation of the perpendicular line that passes through point (10, 2) is: y = ⅕x + 0 or y = ⅕x

User Chris Zielinski
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