Respuesta :
Answer:
(C)4
Step-by-step explanation:
Given the line: [tex]y=\dfrac43 x+1[/tex]
The gradient of the line, [tex]m=\dfrac43[/tex]
A line perpendicular to the given line will have a gradient, [tex]m=-\dfrac34[/tex] (by definition of perpendicularity).
Therefore, a perpendicular line that passes through the point (4,1) is:
[tex]y-y_1=m(x-x_1)\\y-1=-\dfrac34(x-4)\\y-1=-\dfrac34x+3\\y=-\dfrac34x+3+1\\y=-\dfrac34x+4[/tex]
Comparing with the slope-intercept form y=mx+x, the slope of the perpendicular line, b=4.
