Respuesta :
The answer is y=3x+1. So the correct choice is letter choice D.
Answer: The correct option is
(D) [tex]3x-y=-1[/tex]
Step-by-step explanation: We are given to select the equation of a line that is perpendicular to the following line and passing through the point (2, 7) :
[tex]y=-\dfrac{1}{3}x+1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the equation of a line in slope-intercept form is given by
[tex]y=mx+c,[/tex] where m is the slope and c is the y-intercept of the line.
Comparing the above slope-intercept form with equation (i), we get
the slope of the line (i) is
[tex]m=-\dfrac{1}{3}.[/tex]
Let m' be the slope of the required line. Since the product of the slopes of two perpendicular lines is -1, so we must have
[tex]m\times m'=-1\\\\\Rightarrow -\dfrac{1}{3}\times m'=-1\\\\\Rightarrow m'=3.[/tex]
Since the line passes through the point (2, 7), so its equation will be
[tex]y-7=m'(x-2)\\\\\Rightarrow y-7=3(x-2)\\\\\Rightarrow y=3x-6+7\\\\\Rightarrow 3x-y=-1[/tex]
Thus, the required equation of the line is [tex]3x-y=-1[/tex]
Option (D) is CORRECT.
