Question

The equation that passes through (3,6) and is perpendicular to 3x - 4y = - 2

Answer 1

Answer:

C

Step-by-step explanation:

We want the equation of the line that passes through (3, 6) and is perpendicular to:

$3x-4y=-2$

First, convert the second equation into slope-intercept form:

$-4y=-3x-2\Rightarrow \displaystyle y=\frac{3}{4}x+\frac{1}{2}$

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:

$y-y_1=m(x-x_1)$

Substitute:

$\displaystyle y-(6)=-\frac{4}{3}(x-3)$

Distribute:

$\displaystyle y-6=-\frac{4}{3}x+4$

Therefore:

$\displaystyle y=-\frac{4}{3}x+10$

The answer is C.