Question

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

a
y = - 4/3x + 3 1/3
b
y = - 3/4x + 10
c
y = - 4/3x + 10
d
y = 3/4x + 10

Answer 1

C

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=(3)/(4)x+(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)=-(4)/(3)(x-3)`

Distribute:

`\displaystyle y-6=-(4)/(3)x+4`

Therefore:

`\displaystyle y=-(4)/(3)x+10`

The answer is C.