Questions: Write an equation for line L in point-slope form and slope-intercept form. L is perpendicular to y=5x. Write an equation for line L in point-slope form. (Simplify your answer. Use integers or fractions for any numbers in the equation)

Write an equation for line L in point-slope form and slope-intercept form. L is perpendicular to y=5x. Write an equation for line L in point-slope form. (Simplify your answer. Use integers or fractions for any numbers in the equation)
Transcript text: Write an equation for line $L$ in point-slope form and slope-intercept form. $L$ is perpendicular to $y=5 x$. Write an equation for line $L$ in point-slope form. (Simplify your answer. Use integers or fractions for any numbers in the equation)
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Solution

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Solution Steps

Step 1: Find the slope of the perpendicular line

The given line is _y_ = 5_x_. Its slope is 5. Since line L is perpendicular to the given line, the slope of line L is the negative reciprocal of 5, which is -1/5.

Step 2: Identify a point on line L

The graph shows that line L passes through the point (1, 5).

Step 3: Write the equation in point-slope form

The point-slope form of a linear equation is _y_ - _y_₁ = _m_( _x_ - _x_₁), where _m_ is the slope and (_x_₁, _y_₁) is a point on the line. Using the slope -1/5 and the point (1, 5), the equation of line L in point-slope form is _y_ - 5 = -1/5( _x_ - 1).

Final Answer:

_y_ - 5 = -1/5(_x_ - 1)

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