Answer:
C
Step-by-step explanation:
We want the equation of the line that passes through (3, 6) and is perpendicular to:
[tex]3x-4y=-2[/tex]
First, convert the second equation into slope-intercept form:
[tex]-4y=-3x-2\Rightarrow \displaystyle y=\frac{3}{4}x+\frac{1}{2}[/tex]
So, we can see that the slope of the line is 3/4.
The slopes of perpendicular lines are negative reciprocals of each other.
Therefore, the slope of the new line is -4/3.
It passes through the point (3, 6).
We can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute:
[tex]\displaystyle y-(6)=-\frac{4}{3}(x-3)[/tex]
Distribute:
[tex]\displaystyle y-6=-\frac{4}{3}x+4[/tex]
Therefore:
[tex]\displaystyle y=-\frac{4}{3}x+10[/tex]
The answer is C.
