write the equation of the line that is perpendicular to x+2y=12 and goes though the point (-6,-1)

Answer 1

First I would rearrange the equation with y on one side and the rest on the other.

So, starting with x + 2y = 12, we begin unpacking this problem by subtracting x from both sides...

2y = -x + 12

Next, since we need y all by itself, we divide 2 from both sides, giving us...

y = -x/2 + 6 (because 12/2 equals 6).

Now, we see that our slope is actually -1/2 (because that is the number attached to the x and slope-intercept form is written y = mx + b, where y and x are points on the line, m is the slope and b is our intercept - where the line crosses the y-axis).

To find our new slope for our perpendicular line we have to find the negative reciprocal of our original slope (parallel lines have the same slope, but since perpendicular lines will cross each other at a 90 degree angle, they have sort of an opposite slope).

Finding the negative reciprocal isn't as hard as it sounds. We start by simply turning negatives into positives or positives into negatives. In this case, we start with a negative slope, so we will change that slope to a positive one!

m = 1/2, and we're almost done. The reciprocal is our given slope upside down. So we move our denominator to the top of the fraction and our numerator to the bottom. Our new slope is 2/1 or 2!

Next we have to find our new b, or y-intercept, and given the point provided (-6, -1) we can use those x and y values to find the answer for our last variable: b!

So we have our equation of a line with our new slope and we must solve for b after plugging in our x and y values.

y = 2x + b

Plug in the x and y values...

(-1) = 2(-6) + b

Multiply our slope (2) by our x value (-6)...

-1 = -12 + b

Add 12 to both sides, so we have only b on one side of the equation, giving us...

b = 11, because -1 + 12 equals 11 and -12 plus 12 equals 0!

Our last step is to plug in our new slope (m = 2) and our new y-intercept (b = 11) into the slope-intercept form of y = mx + b...

The answer is:

y = 2x + 11

Answer 2

The way I like to do this when the equation is already in standard form is simply 'reverse' the slope to the negative reciprocal changing x + 2y = C into 2x - y = C

So we now have 2x - y = C and we will now put the point (-6,1) in for x and y and see what our value of C is.

2(-6) - (-1) = C

-12 + 1 = C

C = -11

The equation is therefore 2x - y = -11

Now let's see if you can do the other 2 problems you have submitted on your own by following this simple procedure.