Answer: [tex]y+4=-3(x-4)[/tex]
Step-by-step explanation:
- The equation of the line in point-slope form is:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and [tex](x_1,y_1)[/tex] is a point of the line.
- The equation of the line [tex]y=\frac{1}{3}x+4[/tex] is written is slope-intercept form, where the slope is [tex]\frac{1}{3}[/tex].
- By definition, when two lines are perpendicular to each other, the slopes are the negative reciprocals. Therefore, the slope of the perpendicular line must be -3.
- Substitute the point P and the slope -3 into the equation in point-slope form, therefore, you obtain:
[tex]y+4=-3(x-4)[/tex]
