SOLUTION: . Find the equation, in standard form, with all integer coefficients, of the line perpendicular to x + 2y = 8 and passing through (1, -6). Cant figure this one out either, Hel

Algebra ->  Linear-equations -> SOLUTION: . Find the equation, in standard form, with all integer coefficients, of the line perpendicular to x + 2y = 8 and passing through (1, -6). Cant figure this one out either, Hel      Log On


   

Question 77929: . Find the equation, in standard form, with all integer coefficients, of the line perpendicular to x + 2y = 8 and passing through (1, -6).

Cant figure this one out either, Help.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First, it is often helpful to rewrite the given equation (x+2y = 8) in slope-intercept form: y = mx+b
y+=+%28-1%2F2%29x+%2B4 Do yo see how to get this?
Comparing this with the slope-intercept form:
y+=+mx%2Bb you can see that the slope of the given line is %28-1%2F2%29
Now, you will no doubt recall that perpendicular lines have slopes that are the negative reciprocal of each other.
So, the slope of the new line, because it is perpendicular to the given line, will be:2 which is the negative reciprocal of%28-1%2F2%29
Now you can write, for the new line, the equation:
y+=+2x%2Bb But we're not quite done because we need to find the value of b, the y-intercept. We are given the ordered pair of a point (1, -6) through which the new line passes. We can use the x- and y-coordintaes of this point to find the value of b for the new line.
Substitute the x- and y-values from the point into the equation (y= 2x+b) and solve for b.
-6+=+2%281%29+%2B+b Subtract 2 from both sides.
-8+=+b Now we can finish the equation of the new line:
y+=+2x-8
One final step to do because you need your answer in standard form: ax%2Bby+=+c
2x-y+=+8