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]
