Respuesta :

Answer:

[tex]y = -\frac{1}{4}x + c[/tex] --- Slope intercept

[tex]y - y_1 = -\frac{1}{4}(x - x_1)[/tex] --- Point slope

Step-by-step explanation:

Given

Perpendicular to [tex]y = 4x[/tex]

Required

Determine its equation

The general form of an equation is:

[tex]y = mx + c[/tex]

Where

[tex]m = slope[/tex]

By comparison:

[tex]m = 4[/tex]

Next, we calculate the slope of L.

Because L is perpendicular to [tex]y = 4x[/tex], the relationship between their slopes is:

[tex]m_2 = -\frac{1}{m}[/tex]

Substitute 4 for m

[tex]m_2 = -\frac{1}{4}[/tex]

The equation of L in slope intercept form is: [tex]y = mx + c[/tex]

Substitute -1/4 for m

[tex]y = -\frac{1}{4}x + c[/tex]

In point slope form, we have:

[tex]y - y_1 = m(x - x_1)[/tex]

Substitute -1/4 for m

[tex]y - y_1 = -\frac{1}{4}(x - x_1)[/tex]

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