Answer:
(D)5
Step-by-step explanation:
Given a line: [tex]y=\dfrac{3}{4}x+3[/tex]
Comparing with the slope-intercept form y=mx+c
Slope, m [tex]=\dfrac{3}{4}[/tex]
Definition: Two lines are perpendicular if the product of their slopes equals -1.
Therefore, the slope of a line perpendicular to the given line
[tex]m=-\dfrac{4}{3}[/tex]
Therefore, a line that is perpendicular and passes through the point (3,1) is:
[tex]y-y_1=m(x-x_1)\\y-1=-\dfrac{4}{3}(x-3)\\y-1=-\dfrac{4}{3}x+4\\y=-\dfrac{4}{3}x+4+1\\y=-\dfrac{4}{3}x+5[/tex]
Comparing with the slope-intercept from: y=mx+c
The y-intercept of the perpendicular line is therefore 5.
The correct option is D.
