Question

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Explanation:

Find the perpendicular slope

The given line is \(y = 4x\), which has a slope of \(m_1 = 4\).
Since line \(L\) is perpendicular to this line, its slope \(m\) is the negative reciprocal:

$$ m = -\frac{1}{4} $$

Identify the given point

From the graph, line \(L\) passes through the labeled point:

$$ (x_1, y_1) = (1, 4) $$

Write in point-slope form

The point-slope form of a linear equation is:

$$ y - y_1 = m(x - x_1) $$

Substituting \(m = -\frac{1}{4}\) and the point \((1, 4)\):

$$ y - 4 = -\frac{1}{4}(x - 1) $$

Convert to slope-intercept form

To convert to slope-intercept form \(y = mx + b\), solve for \(y\):

$$ y - 4 = -\frac{1}{4}x + \frac{1}{4} $$

$$ y = -\frac{1}{4}x + \frac{1}{4} + 4 $$

$$ y = -\frac{1}{4}x + \frac{17}{4} $$

Answer:

Question 1

Write an equation for line L in point-slope form:

$$y - 4 = -\frac{1}{4}(x - 1)$$

Question 2

Write an equation for line L in slope-intercept form:

$$y = -\frac{1}{4}x + \frac{17}{4}$$