Question

Write an equation for line L in point-slope form and slope-intercept form.

Answer 1

Answer:

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

$y - y_1 = -\frac{1}{4}(x - x_1)$ --- Point slope

Step-by-step explanation:

Given

Perpendicular to $y = 4x$

Required

Determine its equation

The general form of an equation is:

$y = mx + c$

Where

$m = slope$

By comparison:

$m = 4$

Next, we calculate the slope of L.

Because L is perpendicular to $y = 4x$, the relationship between their slopes is:

$m_2 = -\frac{1}{m}$

Substitute 4 for m

$m_2 = -\frac{1}{4}$

The equation of L in slope intercept form is: $y = mx + c$

Substitute -1/4 for m

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

In point slope form, we have:

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

Substitute -1/4 for m

$y - y_1 = -\frac{1}{4}(x - x_1)$