Perpendicular Line Equation

[elysium]

I'm taking an online Adv. Algebra class to catch up on some credits, and I'm stuck on a problem. Here's a full explanation of the problem:

Writing the equation of the line through a given point and perpendicular to a given line

Write an equation for the line that passes through the point (-2, -3) and is perpendicular to the line 2x - 7y = -16.

We first rewrite the given equation in the slope-intercept form:

. . .-7y = -2x - 16

and so

. . .y = 2/7 x + 16/7

The slope of the given equation is 2/7. Since the product of the slopes of two perpendicular lines is -1, the slope of the perpendicular line must be -7/2.

The slope-intercept equation of the perpendicular line is

. . .y = (-7/2)x + b

where the intercept b is yet to be determined. Since the perpendicular line contains the point (-2,-3), it must be the case that

. . .-3 = -7/2 * (-2) + b

Solving this equation for b , we get

. . .b = -10

The line we seek thus has the equation

. . .y = (-7/2)x - 10

which can also be written as

. . .7x + 2y = -20

The answer is 7x + 2y = -20.

Which is all very good, and I do it perfectly until this part:

The line we seek thus has the equation

. . .y = (-7/2)x - 10

which can also be written as

. . .7x + 2y = -20

How do they get that?

 

[pka]

Multiply both sides by 2.
Then add 7x to both sides.

 

[elysium]

Ah, thanks so much! I had a feeling it would be one of those "duh" solutions once I knew the answer.

 

[jonboy]

Ah, thanks so much! I had a feeling it would be one of those "duh" solutions once I knew the answer.

Lol haha I know what ya mean.

 

[Denis]

The line we seek thus has the equation
y= -7/2x- 10
which can also be written as
7x + 2y= -20 .

The term -7/2x is written in a confusing manner;
even if we know it means (-7 divided by 2) multiplied by x,
we have to be careful not to use 2x as the denominator;
I suggest you write these this way: -7x / 2;
then you can easily see that the denominator is 2, so multiply by 2:
2y = -7x - 20