Question

What is the equation of the line that passes through the point ( -1, 1) and is perpendicular to 2x + 4y = 16?

Answer 1

Answer:

B

Step-by-step explanation:

We want the equation of the line that passes through the point (-1, 1) and is perpendicular to:

$2x +4y=16$

Remember that the slopes of perpendicular lines are negative reciprocals of each other.

So, let's find the slope of the original line first. We can do so by converting it to slope-intercept form. Thus:

$4y=-2x+16$

Therefore:

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

The slope is -1/2.

The negative reciprocal of -1/2 is 2.

Thus, the slope of our new line is 2.

The slope is 2 and it passes through the point (-1, 1).

We can use the point-slope form:

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

Substitute:

$y-(1)=2(x-(-1))$

Distribute:

$y-1=2x+2$

Subtracting 2 from both sides yields:

$y-3=2x$

Therefore, our answer is B.